Method and apparatus for generating RF waveforms having aggregate energy with desired spectral characteristics

ABSTRACT

The present invention relates to a method and system that emulates a desired waveform by producing a time profile of the desired waveform, which is characterized by a plurality of sample values, and generating a plurality of RF waveforms, each RF waveform of the plurality of RF waveforms having a polarity and scaled energy based on a corresponding one of the plurality of sample values, to produce an aggregate RF energy having spectral characteristics that approximate the spectral characteristics of the desired waveform.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.60/419,459, filed Oct. 17, 2002, U.S. Provisional Application No.60/432,435, filed Dec. 11, 2002, and U.S. Provisional Application No.60/460,165, filed Apr. 3, 2003, which are incorporated herein byreference.

FIELD OF THE INVENTION

The present invention generally relates to communication systems. Morespecifically, the present invention relates to generating RF waveformshaving desired spectral characteristics.

BACKGROUND OF THE INVENTION

Known communications systems and networks allow wireless devices tocommunicate information over radio frequency (RF) channels. Suchwireless systems, networks, and devices offer many advantages in termsof making information ubiquitously available and easily accessible invarious business and personal applications. Recognizing the benefitsassociated with wireless communication of information, governmentalagencies responsible for frequency spectrum allocation have allocatedspecific frequency bands for such use. For example, in the US, theFederal Communications Commission (FCC) in a 1985 ruling made portionsof the spectrum previously designated for military use, namely, in the915 MHz, 2.4 GHz bands available and designated them as Industrial,Scientific and Medical (ISM) bands for communicating information withouta license. In addition, the FCC allocated portions of the 5 GHz spectrumas the Unlicensed National Information Infrastructure (UNII) band.Making these portions of the frequency spectrum available for unlicenseduse has resulted in proliferation of many types of wirelesscommunication devices ranging from wireless telephones to devices thatoperate within wireless local-area networks (WLANs). Of course, theunlicensed use of the allocated portions of the spectrum remains subjectto FCC regulation, which specifies the rules governing the operationalrequirements within the allocated bands. The operational requirementsare generally defined in terms of allocated spectra and transmission oremission power levels.

Based on the rules promulgated by designated governmental agencies,standardization bodies throughout the world, including ANSI, IEEE, andISO, have developed various standards that specify the requirements forensuring interoperability amongst devices offered by differentmanufacturers. For example, the ANSI/IEEE 802.11 standard defines aprotocol for compatible interconnection of data communication equipmentvia the air, radio, or infrared at specified data rates in local areanetworks, using a carrier sense multiple access protocol with collisionavoidance (CSMA/CA) medium sharing mechanism. The IEEE 802.11 standard,which is hereby incorporated by reference, also specifies a mediumaccess control (MAC) layer that supports operations under control of anaccess point as well as between independent remote stations. Amongst thefunctions performed by the 802.11-specified MAC layer areauthentication, association, re-association services,encryption/decryption procedures, power management, and pointcoordination functions for power coordination.

Other standards known as IEEE 802.11a and IEEE 802.11b, which are alsohereby incorporated by reference, define higher speed physical (PHY)layer extensions in the 5 GHz UNII band and 2.4 GHz ISM band,respectively. The respective PHY layer standards specify the interfacewith the 802.11 MAC layer as well as modulation techniques fortransmitting information within the allocated bands.

The provisions of the IEEE 802.11, 802.11a and 802.11b standards havenow become the blueprints for building local, regional and evennationwide WLANs. These types of WLANs are proliferating to providehigh-speed wireless internet access in such places as airports,hospitals, coffee shops, etc. Each WLAN provides wireless communicationsamong a plurality of devices, including an access point as well asremote stations that are situated within a common area. Generally, eachmobile and access point device, which functions as an interface betweena wireless and a wired network, is equipped with a network interfacecard (NIC) that incorporates MAC and PHY layer circuitry as well asradio frequency circuitry, including antenna circuitry. Other standardsat various stages of development include the 802.11 g and HiperLAN/2standards that provide additional features such as higher data rates andwireless voice over IP capabilities. Also defined are provisions toprovide capabilities amongst mobile wireless stations operating within aplurality of adjacent wireless LANs through access points roaming thatprovide communication coverage for designated areas. This proliferationof wireless devices that operate in the allocated bands and coexistenceamong the many wireless systems and devices has placed substantialburden on the available frequency bands in terms of congestion andinterference.

Bandwidth availability has therefore become an important factor inproliferation and use of wireless devices. Historically, bandwidthavailability, which is regulated by governmental agencies, has beenconstrained primarily because of technological factors. Data ratethroughput is an important parameter in the design of wireless systems.Data rate throughput capability varies proportionally with availablebandwidth but only logarithmically with the available signal to noiseratio (SNR). To achieve high capacity data rate systems within aconstrained bandwidth, complex signal modulations techniques have beenused. Unfortunately, use of such modulation techniques may significantlydecrease SNR.

Typically in such systems, data rate is lowered, often dynamically, forexample, based on a received signal quality criterion, to improvecommunication reliability. Conversely, high data rates are used withreduced reliability. The principle barrier to high data ratecommunications in a wireless local-area network is an interferencephenomenon called “multipath.” A radio signal commonly traverses manypaths as it travels toward a receiver. Multiple propagation paths can becaused by reflections from surfaces in the environment, for example.Some of these paths are longer than others. Therefore, since eachversion of the signal travels at the same speed, some versions of thesignal will arrive after other versions of the signal. Sometimes thedelayed signals will interfere with more prompt signals as the delayedsignals arrive at the receiver, causing signal degradation.

Recent advances in communications technology have enabled ultra-wideband(UWB) systems, which can be used for communications, radar, and/orpositioning. UWB technology holds great promise for a vast array of newapplications that provide significant benefits for public safety,business, and consumers. UWB technology is often referred to as impulseradio technology but may employ any of several types of RF waveforms.Some UWB systems and devices operate by employing very narrow or shortduration pulses having a small number of cycles (e.g., one or twocycles) that result in transmissions having very large bandwidths on theorder of, for example, several GHz. Narrower bandwidth UWBimplementations typically involve wider pulses having many cycles (e.g.,25 to 100) that may have bandwidths on the order of, for example, 500MHz. Generally, with UWB systems, the shorter the pulse duration thelarger the bandwidth, and vice versa.

UWB transmitters and receivers can employ numerous data modulation (anddemodulation) techniques, including amplitude modulation, phasemodulation, frequency modulation, pulse-position modulation (PPM) andM-ary versions of these (e.g., bi-phase, quad-phase, and M-phasemodulation).

Various implementations of impulse radio are described in U.S. Pat. No.4,641,317 (issued Feb. 3, 1987), U.S. Pat. No. 4,743,906 (issued May,10, 1988), U.S. Pat. No. 4,813,057 (issued Mar. 14, 1989), U.S. Pat. No.4,979,186 (issued Dec. 18, 1990), U.S. Pat. No. 5,363,108 (issued Nov.8, 1994), U.S. Pat. No. 5,677,927 (issued Oct. 14, 1997), U.S. Pat. No.5,687,169 (issued Nov. 11, 1997), U.S. Pat. No. 5,812,081 (issued Sep.22, 1998), U.S. Pat. No. 5,832,035 (issued Nov. 3, 1998), U.S. Pat. No.5,952,956 (issued Sep. 14, 1999), and U.S. Pat. No. 6,133,876 (issuedOct. 17, 2000), and U.S. patent application Ser. No. 09/811,326 (filedJul. 20, 2001), U.S. Ser. No. 10/206,648 (filed Jul. 26, 2002), U.S.Ser. No. 60/451,538 (filed Mar. 3, 2003), and U.S. Ser. No. 10/436,646(filed May 13, 2003), all of which are assigned to the assignee of thepresent invention and are incorporated herein by reference.

It has been recognized, however, that the benefits of UWB technologycould be outweighed by its potential to cause harmful interference,particularly with other important radio operations, such as licensedservices. It has also been shown that, under suitable operatingrestrictions, UWB devices may operate using portions of the frequencyspectrum occupied by existing radio services without causing harmfulinterference, thereby permitting scarce spectrum resources to be usedmore efficiently.

Having recognized the promising benefits and potential for harmfulinterference associated with UWB technology, governmental agencies invarious parts of the world have begun cautiously considering andallocating portions of the frequency spectrum for unlicensed use by UWBdevices. For example, the FCC amended Part 15 rules to permit unlicensedoperation of UWB devices. In April 2002, the FCC released a First Reportand Order in connection with Part 15 revisions (In re: Revision of Part15 b of the Commission's Rules Regarding Ultra-Wideband Transmissionssystems (ET Docket 98-153), FCC 0248 document, which is herebyincorporated by reference.)

At the present time, work is in progress for developing standards forexploiting UWB technology. One such effort is by an IEEE working groupunder IEEE 802.15. Information for obtaining all published documents ofthe IEEE standard setting body may be obtained by visiting the IEEEwebsite, www.ieee.com. Briefly, these UWB standards will apply to UWBdevices operating in shared or in non-government frequency bands,including UWB devices operated by U.S. Government agencies. In general,the FCC rules establish corresponding technical standards and operatingrestrictions for various types of UWB devices mainly based on theirpotential to cause interference. For example, outdoors use of UWBdevices are currently restricted to certain imaging systems, hand helddevices, and vehicular radar systems that operate with very low power.In fact, UWB devices with potential for use in high power applications,such as wide-area mobile radio services, are not permitted to operate.

The rules governing operational restrictions are generally specified interms of allocated spectrum, minimum bandwidth, and emission limitationsfor each UWB device type. The rules divide the frequency spectrum intosub-spectrums, with each sub-spectrum being subject to correspondingoperational and emission limitations based on the type of the UWBdevice. For example, ground penetrating radar (GPR) and wall imagingsystems are permitted to operate in the 3.1-10.6 GHz frequency band andthrough-wall imaging systems are permitted to operate in the 1.99-10.6GHz frequency band. Surveillance systems are permitted to operate in the1.99-10.6 GHz frequency band, and medical systems must operate in the3.1-10.6 GHz frequency band. Communication devices are permitted tooperate in the 3.1-10.6 GHz frequency band.

The frequency band of operation of UWB devices is based on the −10 dBbandwidth of the UWB emission. For example, the FCC rules define a UWBdevice as any device where the fractional bandwidth is greater than 0.20or has a minimum bandwidth of 500 MHz, i.e., occupies 500 MHz or more ofspectrum.

At least initially, the adopted rules are significantly stringent.However, the FCC has acknowledged that the initial rules are extremelyconservative and may change in the future as more and more data iscollected regarding UWB emissions. For example, in order to limitunwanted emissions from UWB devices, the FCC has initially adopted moreconservative limits than those imposed on other Part 15 devices. Takinginto account lack of experience with UWB devices, FCC rules regardingUWB emission limits are defined in terms of a reduction to the Part 15general emission levels over defined frequency bands to ensure that UWBdevices have the least possible impact to authorized radio services.Moreover, the emission limits are also designed to ensure that harmfulinterference from the cumulative effect of multiple UWB devices isminimized.

The following table specifies the average emission limits in terms ofdBm EIRP as measured with a one megahertz resolution bandwidth for UWBoperation.

Imaging Imaging, Imaging, Hand held, Frequency below 960 Mid- HighIndoor including Vehicular Band (MHz) MHz Frequency frequencyapplications outdoor radar 0.009-960   §15.209 §15.209 §15.209 §15.209§15.209 §15.209  960-1610 −65.3 −53.3 −65.3 −75.3 −75.3 −75.3 1610-1990−53.3 −51.3 −53.3 −53.3 −63.3 −61.3 1990-3100 −51.3 −41.3 −51.3 −51.3−61.3 −61.3  3100-10600 −51.3 −41.3 −41.3 −41.3 −41.3 −61.3 10600-22000−51.3 −51.3 −51.3 −51.3 −61.3 −61.3 22000-29000 −51.3 −51.3 −51.3 −51.3−61.3 −41.3 Above 29000 −51.3 −51.3 −51.3 −51.3 −61.3 −51.3

FCC rules also allow for the use of various forms of modulation as longas the UWB devices comply with all of the technical standards defined bythe rules. Thus, as long as the transmission system complies with thefractional bandwidth or minimum bandwidth requirements at all timesduring its transmission, it is permitted to operate under the UWBregulations. It is up to the manufacturers of UWB devices to determinehow they will comply with the UWB standards.

The above-mentioned combinations of technical standards and operationalrestrictions are designed to ensure that UWB devices coexist withlicensed radio services without the risk of harmful interference.Clearly, the FCC-promulgated rules are extremely complex, applyingnumerous detailed standards and restrictions to different types of UWBdevices based on their potential to cause harmful interference. Inparticular, FCC rules have been tailored to protect sensitive portionsof the US spectrum from possible UWB interference, e.g., the globalpositioning service (GPS) band. These requirements for different UWBemission levels at different portions of the spectrum in effect createsa “frequency mask” to which UWB devices must be designed.

Additionally, other countries have their own sets of detailed andcomplex spectrum management rules. UWB emission standards established byregulating agencies in other countries will likely have provisionstailored to protect sensitive portions of their spectrum. Becausespectrum allocation and emission standards vary in different regions ofthe world, UWB rules and restrictions are also likely to varysubstantially from region to region. In other words, each country orregion will have its own frequency mask. Furthermore, the variousfrequency masks established for the various countries and regions aresubject to change over time.

Making matters even more complicated is the desire by some manufacturersto protect investments in systems that operate under already definedIEEE standards discussed above, which are not subject to FCC Part 15rules. Indeed, in some cases, UWB emissions restrictions imposed by suchnon-FCC standards may be even more stringent than FCC requirements. Suchnon-FCC-imposed restrictions must also be taken into account whendesigning UWB devices. Accordingly, because frequency masks to which UWBdevices must be designed will vary from country to country and becausethese masks are subject to change as government and industry emissionstandards evolve, there is a need for UWB devices that have theflexibility to vary their emissions to meet the various UWB spectralrequirements.

Moreover, the cost of UWB devices is increasingly becoming a criticalfactor as the use of wireless devices permeates to create a consumerbase that constantly strives for smaller devices having long batterylife. The cost concern becomes even more prevalent if multi-nationalmanufacturers are to maintain multiple inventories of devices that coverdifferent applications and meet country-specific emission requirements.Therefore, there exists a need for UWB devices capable of efficientlyand cost effectively operating under the various frequency masks.

Generally, RF transmission of information requires the creation of an RFcarrier in the transmitter that is modulated with the information. RFreception requires “mixing” the incoming modulated carrier fordemodulation and recovery of the transmitted information. Knownnarrowband systems use fixed-frequency sources for transmission andreception. However, UWB systems require sources that generatefrequencies at a rate on the order of the information rate. One knownUWB system is disclosed in the U.S. Pat. No. 6,026,125, entitled“Waveform Adaptive Ultra-Wideband Transmitter,” issued to Larrick et al.Other prior art methods use fast switching phase locked loops (PLLs),super heterodyne frequency shifting, and frequency-tracking filters forgenerating fixed frequencies at a high rate. However, the implementationof such methods requires complex circuitry, with limitations that makesthem difficult to build on integrated circuits (ICs). A fast-switchingPLL needs a low-jitter voltage-controlled oscillator (VCO) that can betuned to a new frequency very quickly. Generating low-jitter VCO outputat high rate is not easy to accomplish and leads to complex, powerconsuming circuitry. Moreover, highly linear mixers with wide dynamicranges are needed for super heterodyne frequency conversion. Such linearmixers require precision components to achieve balanced operation, whichmakes them difficult to integrate. Frequency-tracking filters,preferably, containing tunable passive or reactive components, (e.g.,capacitors and inductors), are also needed to change the frequency ofoperation. It is well known that passive or reactive components are alsodifficult to integrate. The requirement for rapidly tunable filtersfurther complicates integration.

Primarily, integrated circuit implementation that meets theabove-described requirement should be simple to implement, inexpensiveto produce, and consume as little power as possible. Consequently, it isnecessary to reduce the number of components, particularly thosecomponents that are difficult to integrate with other active circuitry.Further, the cost effective circuit integration requires accounting forcomponent variations both across a single IC as well as from batch tobatch.

SUMMARY OF THE INVENTION

Briefly, the present invention relates to a method and system thatemulates a desired waveform by producing a time profile of the desiredwaveform, which is characterized by a plurality of sample values, andgenerating a plurality of RF waveforms, each RF waveform of theplurality of RF waveforms having polarity and scaled energy based on acorresponding one of the plurality of sample values, to produce anaggregate RF energy having spectral characteristics that approximate thespectral characteristics of the desired waveform. Scaling, in accordancewith the present invention, is to pattern, make, set, regulate, orestimate the energy of each RF waveform of the plurality of RF waveformsaccording to a corresponding sample value of the plurality of samplevalues relative to a reference value. In one embodiment, the referencevalue corresponds to the maximum sample value of the plurality of samplevalues. As such, the present invention addresses the above describedneeds by generating a plurality of RF waveforms based on the timeprofile of the desired waveform, where the desired waveform correspondsto a prototype signal that the plurality of RF waveforms emulate.

In an exemplary embodiment, each of the plurality of RF waveforms has awaveform type, such as an impulse, gaussian pulse, doublet pulse,triplet pulse, step pulse, triangle pulse, sawtooth pulse, or burst ofcycles, and the bandwidth of each of the plurality of RF waveforms spansa frequency band of interest. In accordance with the invention, thepolarity of each RF waveform corresponds to the polarity of acorresponding one the plurality of sample values, and the energy of eachRF waveform of the plurality of RF waveforms is scaled by varying atleast one of amplitude, width or waveform type based on the value of acorresponding one of the plurality of sample values relative to themaximum value of the plurality of sample values. In one embodiment, eachRF waveform of the plurality of RF waveforms can have substantially thesame width, with the polarity and amplitude of each RF waveform beingdetermined based on the value of a corresponding one of the plurality ofsample values relative to the maximum value of the plurality of samplevalues. In an alternative embodiment, each of the plurality of RFwaveforms can have substantially the same amplitude, with theirpolarities and widths being determined based on the value of acorresponding one of the plurality of sample values relative to themaximum value of the plurality of sample values. In another embodiment,both the width and amplitude can be determined based on the value of acorresponding one of the plurality of sample values relative to themaximum value of the plurality of sample values. In a furtherembodiment, the width and amplitude are determined such that a definedamplitude/width ratio is maintained for each RF waveform of theplurality of RF waveforms. In still another embodiment, the waveformtype, or shape, of each RF waveform can be varied in order to achievethe appropriate energy scaling. For example, the number of cycles in RFwaveforms comprising bursts of cycles can be varied.

Preferably, the plurality of the RF waveforms is generated according tothe timing of the sampling of the time profile. Under one arrangementthat is applicable for certain types of RF waveforms, e.g., doubletpulses, the timing of the plurality of RF waveforms can correspond to azero crossing or a crest of each RF waveform. Alternatively, the timingof the plurality of RF waveforms can correspond to an arbitrarilyselected location of each RF waveform, for example, the beginning ofeach RF waveform. As such, the time spacing between the generated RFwaveforms corresponds to the time spacing between the samples of thetime profile. The timing of the plurality of RF waveforms can define adesired center frequency within the frequency band of interest.Moreover, the timing of each RF waveform of the plurality of RFwaveforms can be dithered. The time dithering can be pseudorandom andcan be in accordance with a code. In one embodiment, the timing of eachRF waveform of the plurality of RF waveforms is dithered to suppress atleast one harmonic of the fundamental spectra of the desired waveform.

In an exemplary embodiment, the timing of the plurality of sample valuescan correspond to a Nyquist sampling rate at a frequency within thefrequency band of interest. Alternatively, the sampling rate can begreater than or less than the Nyquist sampling rate, including multiplesor fractions thereof.

According to some of the more detailed features of the presentinvention, the time profile can be produced by an inverse Fouriertransformation of the frequency profile of the desired waveform.

The frequency profile can be defined by frequency, phase, and amplitudeparameters where amplitude or phase is maintained constant over aspecified bandwidth. The frequency profile can include spectralartifacts including a notch, spike, or roll off within the frequencyband of interest and can correspond to a mask such as the one defined bythe FCC to regulate UWB transmissions. The frequency profile can beproduced by a Fourier transformation of a vector amplitude profile ofthe desired waveform.

In one exemplary embodiment, the vector amplitude profile can comprisex, y, z, t, amplitude, and vector polarization angle parameters, wherex, y, and z correspond to location coordinates, and where one or moreparameters of the x, y, z, t, amplitude, and vector polarization angleparameters is maintained constant over time to define a signal amplitudeand polarization at one of a point, line, plane, and surface in spacerelative to a position, for example, a transmit antenna position.

The duration of the time profile can be selected to correspond to thebandwidth of the desired waveform. In one embodiment, the duration ofthe time profile can be selected to correspond to the bandwidth of thefundamental spectra and each one of a plurality of harmonics of thefundamental spectra present in the aggregate RF energy.

In an exemplary embodiment, the desired waveform can correspond to anenveloped sine wave signal having a carrier frequency that correspondsto the center frequency within the frequency band of interest. Theenvelope shape of the sine wave signal can be selected from a cosine,raised cosine, trapezoid, and rectangle, among others. The time profile,including its peak amplitude, can be programmable to produce a desiredenvelope shape. The time profile can have a shifted average DC level. Inone embodiment, the average DC level is shifted such that each of theplurality of sample values has the same polarity. Under one arrangement,a DC component can be removed from the aggregate RF energy by a filter.

Under another arrangement, the time profile of the desired waveform cancorrespond to the time profile of a plurality of orthogonal waveforms.The plurality of orthogonal waveforms can comprise orthogonal waveformsthat are orthogonal when arriving at different times at a receiver. Theorthogonal waveforms can have the same power spectral density profile,but their phase profiles across a frequency span can cause the pluralityof orthogonal waveforms to be orthogonal. For example, the phase of afirst orthogonal waveform can correspond to the phase of a secondorthogonal waveform rotated an even multiple of 2π radians across itsbandwidth. Alternatively, the plurality of orthogonal waveforms can havephase shifts in accordance with a plurality of Walsh functions. Theplurality of orthogonal waveforms can also comprise n orthogonalwaveforms phase shifted by 0 or π radians in accordance with a pluralityof n-bit Walsh functions. Additionally, a first orthogonal waveform ofthe plurality of orthogonal waveforms can be the Hilbert transform of asecond orthogonal waveform of the plurality of orthogonal waveforms.Each orthogonal waveform of the plurality of orthogonal waveforms canalso be an n^(th) order derivative of a first orthogonal waveform of theplurality of orthogonal waveforms.

In another exemplary embodiment, the time profile of the desiredwaveform can be modulated in accordance with at least one of aninformation signal and a code. The time profile of the desired waveformcan be time limited and can be frequency limited.

Moreover, the aggregate energy spectra of the plurality of RF waveformscan be limited to the frequency band of interest, for example, via afilter. Under one arrangement, one or more filters can be used to selectthe fundamental spectra, one or more harmonics, or one or more foldimages. The one or more harmonics and/or one or more fold images can beselected in accordance with a code, which defines a communicationschannel, and can be selected in accordance with an information signal asa form of modulation.

According to one embodiment, the plurality of RF waveforms is generatedin one or more groups, with each group comprising two or more RFwaveforms having a predefined time spacing. Under this arrangement, oneRF waveform in each group can be inverted to selectively eliminate afold image in the frequency band of interest. In a more specificimplementation, the frequency of the fold image corresponds to thegeneration rate of the plurality of RF waveforms, with the predefinedtime spacing corresponding to one fourth of the period of the frequencyof a fold image.

Each of the plurality of RF waveforms can be separately generated as oneof a plurality of digital waveforms or a plurality of analog waveforms.The plurality of analog waveforms can be generated in response to one ormore digital signals of a plurality of digital signals that are storedin a memory.

According to another aspect of the invention, a method for generatingwaveforms includes generating a plurality of RF waveforms at a waveformgeneration rate selected in accordance with a center frequency within afrequency band of interest and modulating the plurality of RF waveformsin accordance with a time profile of a prototype signal to produce anaggregate RF energy that approximates the prototype signal. Theplurality of RF waveforms can be amplitude and/or width modulated inaccordance with the time profile to produce the desired aggregate RFenergy.

According to yet another aspect of the present invention, a waveformgenerator includes a signal generator that generates a plurality of timespaced RF waveforms at a waveform generation rate. The amplitude and/orwidth of each of the plurality of time spaced RF waveforms is inaccordance with a desired envelope. An optional filter limits theaggregate RF energy of the plurality of time spaced RF waveforms towithin a frequency band of interest.

A first signal generator and a second signal generator can be used togenerate a first and second plurality of RF waveforms, with a definedtime spacing between each of the second plurality of ed RF waveforms anda corresponding one of the first plurality of RF waveforms. The firstand second plurality of RF waveforms are amplitude and/or widthmodulated in accordance with the desired envelope. Under onearrangement, the defined time spacing corresponds substantially to onefourth of the period of the frequency of a fold image to be eliminated.

The signal generator can include a constant amplitude (or width) signalgenerator that generates a plurality of constant amplitude (or width)time spaced signals, and an amplitude (or width) modulator thatmodulates the plurality of constant amplitude (or width) time spacedsignals to produce the plurality of time spaced RF waveforms.Alternatively, the signal generator can include a variable amplitude (orwidth) signal generator that separately generates each of said pluralityof time spaced RF waveforms. The amplitudes (or widths) of each of theplurality of variable time spaced RF waveforms can be digitallyrepresented in terms of quantized amplitude (or width) representationsstored in a memory. In one embodiment, the representations arenormalized. The quantized amplitude (or width) representations can thenbe retrieved from the memory to be applied to a digital to analogconverter.

The signal generator can include a variable amplitude variable widthsignal generator that separately generates each of said plurality oftime spaced RF waveforms where both amplitude and width can vary. Theamplitudes and widths of the plurality of time spaced RF waveforms canbe digitally represented in terms of quantized amplitude and widthrepresentations stored in a memory. In one embodiment, therepresentations are normalized. The quantized amplitude and widthrepresentations can then be retrieved from the memory to be applied to adigital to analog converter.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described with reference to theaccompanying figures, wherein:

FIG. 1 illustrates an exemplary frequency band of interest.

FIG. 2 is a diagram of a time profile of an ideal waveform.

FIG. 3 depicts a time profile of an exemplary prototype signal inaccordance with the invention.

FIG. 4 depicts the frequency profile of the exemplary prototype signalof FIG. 3.

FIG. 5 shows a time profile of another exemplary prototype signal.

FIG. 6 depicts the frequency profile of the exemplary prototype signalof FIG. 5.

FIG. 7 shows a time profile of still another exemplary prototype signal.

FIG. 8 is a diagram of the frequency profile of the exemplary prototypesignal of FIG. 6.

FIG. 9 illustrates an exemplary trapezoid enveloped prototype signal.

FIG. 10 depicts the frequency profile of the exemplary trapezoidenveloped prototype signal of FIG. 9.

FIG. 11 shows an exemplary rectangle enveloped prototype signal.

FIG. 12 shows the frequency profile of the exemplary rectangle envelopedprototype signal of FIG. 11.

FIG. 13 presents sampling of the prototype signal of FIG. 3 at theNyquist rate.

FIG. 14 presents the samples of FIG. 13 without the prototype signal.

FIG. 15 presents sampling of the prototype signal of FIG. 3 at theNyquist rate with a different sample alignment than shown in FIG. 13.

FIG. 16 presents the samples of FIG. 15 without the prototype signal.

FIG. 17 illustrates sampling of the prototype signal of FIG. 3 at a ratethat is less than the Nyquist rate.

FIG. 18 shows the samples of FIG. 17 without the prototype signal.

FIG. 19 depicts sampling of the prototype signal of FIG. 3 at a ratethat is greater than the Nyquist rate.

FIG. 20 presents the samples of FIG. 18 without the prototype signal.

FIG. 21 presents a comparison of the frequency profile of FIG. 4 to thefrequency profile of RF waveforms generated in accordance with thesamples of FIGS. 13 and 14.

FIG. 22 presents a comparison of the frequency profile of FIG. 4 to thefrequency profile of RF waveforms generated in accordance with thesamples of FIGS. 15 and 16.

FIG. 23 presents a comparison of the frequency profile of FIG. 4 to thefrequency profile of RF waveforms generated in accordance with thesamples of FIGS. 17 and 18.

FIG. 24 presents a comparison of the frequency profile of FIG. 4 to thefrequency profile of RF waveforms generated in accordance with thesamples of FIGS. 19 and 20.

FIG. 25 illustrates exemplary impulses generated in accordance withsamples of the prototype signal at a 2 GHz sampling rate.

FIG. 26 shows the frequency profile of the impulses of FIG. 25.

FIG. 27 depicts exemplary doublets generated in accordance with samplesof the prototype signal at a 2 GHz sampling rate.

FIG. 28 shows the frequency profile of the doublets of FIG. 27.

FIG. 29 illustrates exemplary triplets generated in accordance withsamples of the prototype signal at a 2 GHz sampling rate.

FIG. 30 shows the frequency profile of the triplets of FIG. 29.

FIG. 31 illustrates exemplary gaussian pulses generated in accordancewith samples of the prototype signal at a 2 GHz sampling rate.

FIG. 32 shows the frequency profile of the gaussian pulses of FIG. 31.

FIG. 33 depicts exemplary triangle pulses generated in accordance withsamples of the prototype signal at a 2 GHz sampling rate.

FIG. 34 shows the frequency profile of the triangle pulses of FIG. 33.

FIG. 35 depicts width modulated square wave pulses in accordance with anembodiment of the invention.

FIG. 36 shows the frequency profile of the width modulated square wavepulses of FIG. 35.

FIG. 37 presents the ‘zoomed out’ frequency profile of FIG. 21.

FIG. 38 presents the filtered waveform produced by limiting the energyof the frequency profile of FIG. 37 to the frequency band of interest.

FIG. 39 presents an exemplary waveform generator in accordance with anembodiment of the invention.

FIG. 40 depicts an exemplary harmonic of the fundamental spectra of RFwaveforms generated in accordance with the invention.

FIG. 41 illustrates sampling of an exemplary prototype signal.

FIG. 42 depicts fundamental spectra, harmonics, and fold images in thefrequency profile of RF waveforms generated in accordance with thesamples shown in FIG. 41.

FIG. 43 presents the filtered waveform produced by limiting the energyof the frequency profile of FIG. 42 to the frequency band of interest.

FIG. 44 illustrates sampling of the exemplary prototype signal of FIG.41 at a different sampling rate.

FIG. 45 depicts a fold image present inside the frequency band ofinterest.

FIG. 46 illustrates the filtered waveform produced by limiting theenergy of the frequency profile of FIG. 45 to the frequency band ofinterest.

FIG. 47 presents sampling of the exemplary prototype signal of FIG. 41using sample pairs.

FIG. 48 illustrates the elimination of the fold image previously shownin FIG. 45 to be inside the frequency band of interest.

FIG. 49 presents the filtered waveform produced by limiting the energyof the frequency profile of FIG. 48 to the frequency band of interest.

FIG. 50 presents waveform generators in accordance with one embodimentof the invention.

FIG. 51 illustrates the inverting of one sample of each of the samplepairs of FIG. 47.

FIG. 52 depicts the elimination of the fundamental spectra in accordancewith one embodiment of the invention.

FIG. 53 presents the filtered waveform produced by limiting the energyof the frequency profile of FIG. 52 to the frequency band of interest.

FIG. 54 depicts sampling of the prototype signal of FIG. 41 at the 2 GHzrate.

FIG. 55 shows uses of fundamental spectra, harmonics, and fold images toproduce multi-band signals.

FIG. 56 is an exemplary transmitter and direct conversion receiver.

FIG. 57 depicts an exemplary transceiver.

FIG. 58 shows an alternative waveform generator in accordance with anembodiment of the invention.

FIG. 59 presents a receiver in accordance with an embodiment of theinvention.

FIG. 60 present another receiver in accordance with another embodimentof the invention.

FIG. 61 illustrates a receiver in accordance with an embodiment of theinvention.

FIG. 62 depicts a receiver in accordance with an embodiment of theinvention.

FIG. 63 depicts a circuit in accordance with an embodiment of theinvention.

FIG. 64 depicts another circuit in accordance with another embodiment ofthe invention.

FIG. 65 presents a multi-band transmitter embodiment of the invention.

FIG. 66 illustrates a multi-band receiver embodiment of the invention.

FIG. 67 shows a multi-band waveform generator in accordance with analternative embodiment of the invention.

FIG. 68 presents another multi-band waveform generator in accordancewith the invention.

FIG. 69 presents the primary display of the Waveform Synthesis Analyzersoftware.

FIG. 70 presents another display of the Waveform Synthesis Analyzersoftware.

FIG. 71 depicts another display of the Waveform Synthesis Analyzersoftware.

DETAILED DESCRIPTION OF THE INVENTION

Foreword

The invention described herein is believed to be a truly pioneeringinvention that can be likened to the discovery of Calculus. As Calculusmade complex mathematical abstraction possible, the current inventionmakes the generation of RF waveforms having desired spectralcharacteristics possible. It is believed, that as Calculus enabled anentirely new mathematical paradigm, the present invention enables anentirely new paradigm in radio communications.

Applications of the Present Invention

The present invention can be used to produce RF waveforms compatiblewith any type of narrowband, wideband or ultra-wideband device. Suchdevices include, but are not limited to, those that produce multi-band,pulse, RF burst, and continuous RF signals. An exemplary system inaccordance with the present invention can be used in various types ofUWB communication devices where one or more aspects of an UWB waveformis modulated such as its amplitude, phase, frequency, or position intime. UWB-enabled communications may involve tethered or un-tetheredimplementations. For example, UWB transmitters, receivers, and/ortransceivers can be used to provide wireless communications between aset-top box and a portable television, where the set-top box receivestelevision signals via a cable infrastructure that are conveyed via UWBdevices to the portable television. Information may also be conveyedfrom the portable television to the set-top box. Similarly, UWB devicescan be used to provide communications between a network hub and aportable laptop personal computer or a personal digital assistant (PDA)device. Generally, UWB devices can be used to convey analog and/ordigital information between tethered and un-tethered devices such ascomputers, printers, cameras, sensors, phones, gaming devices, PDAs,home appliances, meters, etc. Examples of various applications involvingUWB communications may be found in U.S. Pat. Nos. 6,351,652, 6,354,946,6,492,904, and 6,512,455 and U.S. patent application Ser. Nos.09/407,115,09/436,234, 09/501,372, 09/694,647, 09/709,867, 09/750,822,and 10/225,298, all of which are assigned to the assignee of the presentinvention and are incorporated herein by reference.

An exemplary system in accordance with the present invention can be usedin various types of radar devices. Examples of UWB radar devices includeground penetrating radar (GPR), wall imaging, through-wall surveillance,medical imaging devices, and vehicular radar systems. Usually, GPRoperates in contact with, or within close proximity to, the ground.Objects such as pipes, rocks, minerals, oil, etc. are detected byemitting pulses into the ground and evaluating signal reflections, orreturns, received from the objects. Wall-imaging systems are designed todetect the location of objects contained within a “wall,” such as aconcrete structure, the side of a bridge, or the wall of a mine.Surveillance systems operate as “security fences” by establishing astationary RF perimeter field and detecting the intrusion of persons orobjects in that field. A medical imaging system may be used for avariety of health applications to “see” inside the body of a person oranimal. Vehicular radar devices are able to detect the location andmovement of objects near a vehicle, enabling features such as nearcollision avoidance, improved airbag activation, and suspension systemsthat better respond to road conditions. Generally, UWB radar operates bytransmitting pulses and detecting a signal reflecting off an objectafter one or more predetermined time delays corresponding to one or moredistances from the UWB transmitter to the object and from the object tothe UWB receiver. UWB radar may be mono-static or bi-static meaning thetransmitter and receiver may be in the same location or in separatelocations. Bi-static implementations may also involve multiple transmitantennas and/or multiple receive antennas. Examples of variousapplications involving UWB radar may be found in U.S. Pat. Nos.6,177,903, 6,218,979, 6,462,701, and 6,614,384, and U.S. patentapplication Ser. Nos. 09/998,480, and 10/083,191, all of which areassigned to the assignee of the present invention and are incorporatedherein by reference.

An exemplary system in accordance with the present invention can be usedin various types of positioning systems. Examples include systems fortracking assets such as cargo, inventory, or luggage, systems fortracking emergency personnel such as firemen, and systems for trackingpersons or objects within a mall, amusement park, grocery store, etc.Such systems typically involve reference impulse radios having knownpositions and mobile impulse radios attached to an asset, object, personor animal. Various architectures can be employed involving simplex orduplex communications between the reference and mobile radios where thethree dimensional location of a mobile radio can be determined relativeto known positions of the reference radios to within a few centimeters.Examples of various UWB positioning systems, architectures, andapplications may be found in U.S. Pat. Nos. 6,133,876, 6,111,536,6,300,903, and 6,483,461 and U.S. patent application Ser. Nos.09/511,991, 09,619,295, 09/642,892, 09/694,151, and 09/710,679, all ofwhich are assigned to the assignee of the present invention and areincorporated herein by reference.

UWB systems may also involve a combination, or fusion, ofcommunications, radar, and/or positioning location and tracking (PLT)capabilities where a single UWB transceiver is used for all neededfunctions. For example, an UWB-enabled robot may employ UWB radar todetect objects within its proximity. An UWB-enabled object, such as arobot, may be controlled based on its position relative to referenceradios and may receive commands and transmit information such as sensordata using UWB communications. Examples of UWB systems involving thefusion of communications, radar, and/or PLT may be found in U.S. Pat.Nos. 6,466,125, 6,469,628, 6,489,893, 6,492,206, 6,501,393, and6,504,483 and U.S. patent application Ser. Nos. 09/710,679, 09/760,922,09/873,439, and 09/873,968, all of which are assigned to the assignee ofthe present invention and are incorporated herein by reference.

Because UWB (and non-UWB) devices may be employed in such a wide varietyof applications, the present invention is intended to generate a widevariety of RF waveforms having a wide variety of spectralcharacteristics, for example, to accommodate government rules andregulations, industry standards, and application-specific requirements.In compliance with FCC rules, through-wall imaging systems andsurveillance systems made in accordance with the present invention mayoperate with a minimum bandwidth within the 1990-10,600 MHz frequencyband while higher frequency imaging devices and hand held devices mightoperate within the 3100-10,600 MHz frequency band. Similarly, vehicularradar systems may operate within the 22-29 GHz frequency band and with acarrier frequency greater than 24.075 GHz. However, any other suitabledevice type, requiring different spectral characteristics may operate inaccordance with the present invention.

In an exemplary system, the bandwidth is determined based on −10 dBemission points and the center frequency of the UWB emission. However,depending on other considerations, including practicality andmeasurement accuracy, emission points may be set at any suitable level,e.g., −5 dB or −15 dB. In an exemplary embodiment, the UWB devicesoperating within the system have a fractional bandwidth or a minimumbandwidth. The fractional bandwidth is defined by 2(fH-L)/(fH), where fHis the upper frequency of the specified emission point and fL is thelower frequency of the specified emission point. The center frequency ofthe transmission is determined based on the average of the upper andlower of the specified emission points, i.e., (f_(H)+f_(L))/2. It shouldalso be noted that in some UWB systems, there is no clear centerfrequency as with other modulation techniques, such as AM and FM.Furthermore, the shape of the transmitted spectrum may be significantlymodified by the frequency response of the antenna such that even thecarrier frequency, where employed, may not represent the centerfrequency.

For the purpose of discussion, the fractional bandwidth is selected tobe greater than 0.20 and the minimum bandwidth is selected to be greaterthan or equal to 500 MHz. In other words, the UWB devices transmitsignals that occupy 500 MHz or more of the allocated spectrum. However,it should be noted that depending on application, any other suitablefractional bandwidth ranges, e.g., 0.15, 0.17, 0.25, may be used. Also,the minimum bandwidth may be set to other values, ranging from tens orhundreds of MHz to a few GHz. It should be noted that transmissionsystems are not precluded from UWB definition simply because thebandwidth of the emission is due to a high-speed data rate instead ofthe width of the pulse or impulse.

Emission limits in the system of the present invention are based on theequivalent of a power spectral density, i.e., a field strength limit isspecified along with a measurement bandwidth. Preferably, the radiatedlimits below 1 GHz are based on measurements employing a quasi-peakdetector that effectively provides an average reading with someweighting for peak signal levels. The radiated emissions limits for bothintentional and unintentional radiators above 1 GHz are based onmeasurements using an average detector. However, intentional radiatorsmay also be subject to a requirement that the total peak levels ofemissions above 1 GHz be no greater than a specified level, e.g., 20 dBabove the average limits.

An exemplary system according to the present invention supports emissionlimits for various portions of the allocated UWB spectrum in absoluteterms or in relative terms. In one embodiment, the relative termscorresponds to specified emission limits, e.g., the general emissionslimits of the FCC Part 15. For example, some types of UWB devices, e.g.,GPRs, may operate with the specified minimum bandwidth below 960 MHz atthe Part 15 general emission limits while attenuating emissions in the960-1610 MHz below the general limits by a defined amount, e.g., 24 dB.Furthermore, the present invention supports high level attenuation ofnarrowband emissions in the GPS below the general limits by largeamounts, e.g., 34 dB. Emissions in the 1610-1990 MHz may be attenuatedbelow the general limits by yet another amount, e.g. 12 dB, whileemissions above 1990 MHz may be attenuated below the general limits bystill another amount, e.g., 10 dB. Other UWB device type, e.g., handhelddevices, can operate within the band from 3100 MHz to 10,600 MHz at thePart 15 general emission limits, while ensuring emissions below 960 MHzdo not exceed the general limits and emissions in the 960-1610 MHz bandare attenuated below the general limits by specified levels, e.g., 24dB. Again, narrowband emissions in the GPS band can be attenuated belowthe general limits by larger degrees, e.g., 34 dB to protect GPSdevices. In short, the present invention can support a wide variety ofemission limits for specified UWB device types within differentfrequency bands for indoor and outdoor applications.

Still another type of UWB device, for example, vehicular radar systems,operates with the specified minimum bandwidth within the 22-29 GHz bandand with the center frequency and the frequency at which the maximumemission occurs both located above 24.075 GHz. According to thisembodiment, emissions below 960 MHz do not exceed the general limits,emissions in the 960-1610 MHz band are attenuated below the generallimits by 34 dB; narrowband emissions in the GPS bands are attenuatedbelow the general limits by 44 dB; emissions in the 1610-22,000 MHz bandand in the band above 3.1 GHz are attenuated below the general limits by20 dB; and emissions between 29 GHz and 31 GHz are attenuated below thegeneral limits by 10 dB.

The present invention may be used with any type of narrowband, widebandor ultra-wideband device, including but not limited to the types of UWBdevices described above. Such devices include, but are not limited to,those that produce multi-band, pulse, RF burst, and continuous RFsignals. Exemplary embodiments that may use the waveform generationtechnique of the present invention may employ any type of modulationincluding, but not limited to, frequency, amplitude, phase, position(e.g., PPM), Single Side Band (SSB), Double Side Band (DSB) or othertypes of modulation. However, it should be noted that modulation is notrequired for practicing the invention. Also, the present invention maybe used in systems that utilize a wide variety of multiple accessmethods, such as FDMA, CDMA, TDMA, or any combination thereof.

Emulation of Desired Waveform

According to one aspect, the present invention relates to a system andmethod that emulate a desired waveform. The present invention emulatesthe desired waveform by generating a plurality of RF waveforms havingaggregate energy that approximates the energy of the desired waveform tomeet a wide range of spectral requirements including those of exemplaryapplications given above. Such requirements may be defined in terms of amask and be characterized by various energy level or power emissiondistributions across a desired frequency spectrum. In one exemplaryembodiment, the RF waveforms generated in accordance with the presentinvention together have a bandwidth of at least 500 MHz within afrequency band spanning from 1.9 GHz to 10.6 GHz, as defined by the nowamended FCC Part 15 requirements.

The desired waveform has a time profile that can be characterized by aplurality of sample values. The polarity of each generated RF waveformof the plurality of RF waveforms is in accordance with the plurality ofa corresponding one of the plurality of sample values of the timeprofile. The energy contained in each generated RF waveform of theplurality of RF waveforms is scaled according to a corresponding one ofthe plurality of sample values of the time profile to produce anaggregate RF energy that approximates the spectral characteristics ofthe desired waveform. In other words, the present invention emulates thedesired waveform to fill a spectrum within a frequency band of interestwith aggregate RF energy that approximates the spectral characteristicsof the desired waveform.

The energy of each RF waveform can be scaled by patterning, making,setting, regulating, representing or estimating the energy of each RFwaveform of the plurality of RF waveforms according to a correspondingsample value of the plurality of sample values relative to a referencevalue. For example, the reference value can corresponds to the maximumsample value of the plurality of sample values. For scaling purpose, thesample values may be normalized against the maximum sample value. Theenergy of each RF waveform can be scaled by varying one or anycombination of the width, amplitude or type of the RF waveform. Asherein described, the term amplitude can represent voltage or current.

In an exemplary embodiment, the present invention achieves the desiredspectral characteristics by scaling the root mean squared (RMS)amplitudes of each of the plurality of RF waveforms, where the timing ofthe sample values of the time profile corresponds to the nominal timingof the generated plurality of RF waveforms. According to the presentinvention, the RMS amplitude of each RF waveform may be scaled byvarying the width, amplitude and/or type of the waveform where theamplitude can be voltage or current.

In one embodiment, the time profile is sampled at the Nyquist rate,which is two times the carrier frequency. In another embodiment of theinvention, the time profile is sampled at a rate greater than theNyquist rate, for example, 2×Nyquist. In a further embodiment, the timeprofile is sampled at a rate less than the Nyquist rate, which isreferred to by the inventors as sub-sampling and is described furtherbelow. The time profile can also be sampled at any fraction of theNyquist rate.

It should be noted that the present invention has been simulated usingsoftware having variables that control and support analysis of theinvention. The software, referred to as the Waveform Synthesis Analyzer,was developed using the Borland Delphi™ programming language to executeunder the Windows™ operating system on a Pentium™-based personalcomputer. Many of the figures included herein were generated using theWaveform Synthesis Analyzer, which is further described later in thisspecification.

The Desired Waveform

As stated above, the present invention generates a plurality of RFwaveforms that emulate a desired waveform. Typically, a transmitted RFsignal must have spectral characteristics that fall within allowablespectral boundaries such as spectral requirements defined by governmentrules and regulations and/or industry standards. Ideally, thetransmitted waveform would have a power spectral density (PSD) across afrequency band of interest that is exactly equal to what is permitted byspectral requirements, in which case the transmitted waveform could bereferred to as an ideal waveform. However, generating such an idealwaveform using conventional techniques could require complex andexpensive circuitry. Consequently, it may be more practical andtherefore more desirable to produce a simpler waveform having spectralcharacteristics similar to those of the ideal waveform, or a part of theideal waveform, which satisfy spectral requirements instead of exactlymeeting them. The inventors refer to such a waveform as the desiredwaveform. Thus, the desired waveform can be selected to satisfy definedspectral requirements. As such, the desired waveform can be used todefine a plurality of RF waveforms that when generated have aggregateenergy that approximates the energy of the desired waveform had it beengenerated. Thus, the aggregate energy spectra of the generated RFwaveforms corresponds to the spectral characteristics of the desiredwaveform.

The Frequency Profile

A frequency profile can be used to characterize spectral requirementsand can be defined by frequency, phase, and amplitude parameters.Amplitude or phase parameters can be maintained constant over aspecified bandwidth. Typically, phase is held constant. The frequencyprofile can be characterized by the fundamental spectra of a transmittedwaveform (or waveforms), harmonics of the fundamental spectra, and foldimages of the fundamental spectra and the harmonics. The frequencyprofile may include a frequency band of interest. The frequency profilecan also include spectral artifacts including a notch, spike, or rolloff within the frequency band of interest or it can correspond to a masksuch as the one defined by the FCC to regulate UWB transmissions.

FIG. 1 shows an exemplary frequency profile of spectral requirements fora frequency band of interest 10 centered at 4 GHz with a 500 MHzbandwidth. In an ideal case, the transmitted waveform would ‘fill theband’ such that the PSD of the transmitted signal would be exactly equalto what is permitted by the spectral requirements.

One skilled in the art will recognize that a frequency band of interestmay have power limitations that vary across the band. For example, thefrequency band in which UWB signals are allowed spans across 1.9 GHz to10.6 GHz and has various power constraints for different portions of theband, as previously described. Thus, the frequency profile used inaccordance with the invention might correspond to a frequency mask suchas the FCC mask governing UWB transmissions that spans the 1.9 GHz to10.6 GHz frequency band or the frequency profile might correspond to aportion of a frequency mask such as the 3.1 GHz to 10.6 GHz portion ofthe FCC UWB mask to be used by ground penetrating radar systems.

The Time Profile

As stated above, the present invention produces a plurality of RFwaveforms based on samples of a time profile of the desired waveformsuch that the aggregate energy spectra of the plurality of RF waveformssatisfies various frequency and energy profile requirements. In apreferred embodiment, a time profile plots voltage versus time, althougha time profile may alternatively plot current, power or energy versustime. A time profile can be produced by an inverse Fouriertransformation of a frequency profile or otherwise produced.

FIG. 2 shows the time profile of an exemplary ideal waveform thatsubstantially fills the frequency band of interest 10 of FIG. 1. Theideal waveform comprises an amplitude-modulated sine wave having a 4 GHzcarrier frequency that was produced by an inverse Fourier transformationof the frequency profile of FIG. 1, which has a 4 GHz center frequency.As shown, the ideal waveform has an exemplary envelop comprising a mainlobe 20 and a plurality of side lobes 22.

In FIG. 2, the duration of the main lobe 20 is 4 nsec, which roughlycorresponds to the 500 MHz bandwidth of the frequency band of interest10 of FIG. 1. Although FIG. 2 shows six side lobes 22 (three on eachside of the main lobe), the ideal waveform has additional smaller andsmaller side lobes ad infinitum that are not shown. One skilled in theart would recognize that various other waveforms having suitable timeprofiles could also be produced that substantially meet numerousfrequency profile requirements within any frequency band of interest 10.

Vector Amplitude Profile

In another embodiment, the frequency profile can be produced by aFourier transformation of a vector amplitude profile of the desiredwaveform. The vector amplitude profile can comprise x, y, z, t,amplitude, and vector polarization angle parameters, where x, y, and zcorrespond to location coordinates, and where one or more parameters ofthe x, y, z, t, amplitude, and vector polarization angle parameters ismaintained constant over time to define a signal amplitude andpolarization at one of a point, line, plane, and surface in spacerelative to a position, for example, a transmit antenna position. Afrequency profile derived from a vector amplitude profile can then beused to produce a time profile of the desired waveform as previouslydescribed.

Prototype Signals

As stated previously, a desired waveform can be generated as a simpler,less expensive alternative to generating an ideal waveform. For example,to substantially fill the 500 MHz frequency band of interest 10 of FIG.1, a desired waveform may correspond to the main lobe 20 of the idealwaveform of FIG. 2, since the main lobe contains the majority of theenergy of the ideal waveform. According to the invention, the desiredwaveform is modeled using a prototype signal corresponding to thedesired waveform. The prototype can be the same as or representative ofthe desired waveform. In one embodiment of the present invention, adesired waveform is emulated by a plurality of RF waveforms defined bysamples of the time profile of a prototype signal corresponding to thedesired waveform.

Generally, the bandwidth of the prototype signal is defined by its shapeand duration. Its shape also defines the characteristics of its sidelobes. Often, it is desirable that the energy of the largest side lobebe 20 to 25 dB below the peak power of the main lobe in order to providea desirable carrier-to-noise ratio. Furthermore, for channelizationpurposes, it may be desirable to minimize overlapping of the main lobeinto adjoining frequency bands. One skilled in the art will appreciatethat certain envelope shapes can have certain advantages over othersdepending on the conditions under which a signal is to be transmittedand received and that selection of prototype signal characteristics mayinvolve various tradeoffs.

The prototype signal can be a sine wave signal, chirped signal, pulsesignal, or any other form of signal that has desired spectralcharacteristics, including a noise-like signal. If the prototype signalis a sine wave signal, its center frequency is defined by its carrierfrequency, whereas alternative forms of a prototype signal may not havea carrier. The shape of the prototype signal may be defined by anenvelope although it is not necessary for the prototype signal to bedefined by an envelope to practice the invention. A suitable envelopeshape might be a half cosine, raised half cosine, trapezoid, rectangle,Gaussian, or any other desired shape. Under the present invention, anysuitable combination of carrier frequency, shape and duration may bechosen for a prototype signal to achieve desired spectralcharacteristics so long as it has spectral energy across the frequencyband of interest.

In one exemplary embodiment of the invention, the prototype signal 30comprises a sine wave signal as shown in FIG. 3, which has a 4 GHzcarrier and is amplitude-modulated by a raised half cosine envelope.This envelope can be chosen for its optimization of burst brevity in thetime domain and narrow bandwidth in the frequency domain. To achieve anexemplary frequency profile having a −10 dB bandwidth of 500 MHz, theduration, or width, of the raised half cosine envelope is chosen to be 4ns. One skilled in the art will recognize that the prototype signal 30of FIG. 3 is representative of the main lobe 10 of FIG. 2 and that theprototype signal 30 could alternatively be the same as the main lobe 10of FIG. 2 or be otherwise representative of the main lobe 10 of FIG. 2.One skilled in the art will recognize that the prototype signal of FIG.3 varies from −1.0 v to 1.0 v about a 0.0 v reference value and willunderstand that these values were chosen merely to simplify presentingthe invention. Generally, the time profile of the prototype signal canhave whatever values are desirable, and characteristics such as symmetryor normalization of the example prototype signals provided herein arenot intended to limit the scope of the invention. For example, theprototype signal shown in FIG. 3 could be shifted such that it variesfrom 0.0 v to 2.0 v about a 1.0 v reference value and the prototypesignal could also resemble a noise signal or have any other desiredshape.

FIG. 4 depicts the frequency profile 40 for the prototype signal 30 ofFIG. 3. For comparison purposes, a 500 MHz wide frequency band ofinterest 10 centered at 4 GHz of FIG. 1 overlies the frequency profile40. By comparing the frequency profile 40 to the frequency band ofinterest 10 it is clear that the prototype signal of FIG. 3substantially fills the frequency band of interest 10, where only theupper left and upper right corners of the frequency band of interest 10are not filled. One skilled in the art will also recognize that the −10dB bandwidth of the prototype signal 30 is 500 MHz, which defines an UWBwaveform according to FCC rules. The frequency profile in FIG. 4 alsoshows the peak power of the largest side lobe 42 to be approximately 23dB below the peak power of the main lobe 44.

FIG. 5 shows another example of a raised half cosine-enveloped sine waveprototype signal 50 having the same 4 ns duration as the prototypesignal 30 of FIG. 3, but having a carrier frequency of 3 GHz. FIG. 6presents the frequency profile 60 of the prototype signal 50 of FIG. 5,which has a −10 dB bandwidth of 500 MHz and a center frequency of 3 GHz.By comparing FIG. 4 and FIG. 6 it can be seen that the frequencyprofiles 40, 60 of the prototype signals of FIG. 3 and FIG. 5 are thesame except for their center frequencies. Similarly, FIG. 7 provides athird example of a raised half cosine-enveloped sine wave prototypesignal 70 having the same 4 ns duration as the prototype signals 30, 50of FIG. 3 and FIG. 5, but having a carrier frequency of 5 GHz. FIG. 8presents the frequency profile 80 of the prototype signal of FIG. 7,which has a −10 dB bandwidth of 500 MHz and a center frequency of 5 GHz.By comparing FIG. 4, FIG. 6 and FIG. 8 it is evident that the frequencyprofiles 40, 60, 80 of the prototype signals 30, 50, 70 of FIG. 3, FIG.5 and FIG. 7 are the same except for their center frequencies.Therefore, in the above examples, the aggregate energy of the RFwaveforms that emulates the energy of a corresponding prototype signalsubstantially fills a 500 MHZ band of interest centered at a centerfrequency defined by the carrier frequency of the prototype signal.

FIG. 9 depicts an exemplary embodiment of a prototype signal 90comprising a trapezoid-enveloped sine wave having a carrier frequency of4 GHz. For comparison purposes, the duration of the envelope is 4 ns,which is the same duration as the raised half cosine envelope 30 of FIG.3. FIG. 10 presents the frequency profile 100 of the prototype signal 90of FIG. 9, which has a center frequency of 4 GHz, a −10 dB bandwidth ofabout 600 MHz, and a largest side lobe 102 having peak powerapproximately 26 dB below the peak power of the main lobe 104. Whencomparing frequency profile 100 to the frequency profile 40 of FIG. 4,it is evident that the trapezoid envelope results in a somewhat moredesirable carrier-to-noise ratio than the raised half cosine envelopebut has a greater tendency to overlap into adjoining bands. One skilledin the art will also recognize that to achieve a 500 MHz bandwidth at−10 dB, the duration of the envelope could be increased, which couldreduce channelization.

FIG. 11 depicts an exemplary embodiment of a prototype signal 110comprising a rectangle-enveloped sine wave having a carrier frequency of4 GHz. Again, for comparison purposes, the duration of the envelope is 4ns, which is the same duration as the raised half cosine envelopedprototype signal 30 of FIG. 3 and the trapezoid enveloped prototypesignal 90 of FIG. 9. FIG. 12 presents the frequency profile 120 of theprototype signal 110 of FIG. 11, which has a center frequency of 4 GHz,a −10 dB bandwidth of about 400 MHz, and a largest side lobe 122 havingpeak power approximately 13 dB below the peak power of the main lobe124. When comparing FIG. 12 to FIG. 4 and FIG. 10 it is evident that therectangle envelope results in a less desirable carrier-to-noise ratiobut has a lesser tendency to overlap into adjoining bands. One skilledin the art will also recognize that to achieve a 500 MHz bandwidth at−10 dB, the duration of the envelope could be decreased, which couldimprove channelization.

Thus, FIGS. 3 through 12 illustrate the time and frequency profiles ofalternative prototype signals that can produced that are representativeof a desired waveform corresponding to the main lobe 20 of the idealwaveform of FIG. 2 to appropriately fill the frequency band of interest10 of FIG. 1 and to meet other desired spectral requirements such as adesired carrier-to-noise ratio or a requirement to minimize overlappinginto adjoining bands. Generally, in accordance with the invention, aprototype signal can be defined having desired spectral characteristics.

In one embodiment of the invention, the time profile of the prototypesignal has a shifted average DC level such that the average DC level isnon-zero. Under one arrangement, the average DC level can be shiftedsuch that samples of the time profile of the prototype signal have thesame polarity. Then, a DC component can be removed from the aggregate RFenergy by a filter.

Sampling the Time Profile

According to the invention, a plurality of RF waveforms is defined bycorresponding samples of the time profile of the prototype signal, whichcorresponds to the desired waveform, where the polarity, relativeenergy, and timing of each of the plurality of RF waveforms correspondsto the polarity, relative magnitude, and timing of a correspondingsample of the time profile.

In one embodiment of the invention, the time profile of the prototypesignal is sampled at the Nyquist rate, which is twice the carrierfrequency. FIG. 13 depicts sampling of the time profile of the prototypesignal 30 of FIG. 3 at the Nyquist rate of 8 GHz. In FIG. 13, thesamples 130 are shown to coincide with the crests 132 of the prototypesignal 30. However, this alignment is not required. The samples can beshifted forward or backward in time to align at any location on the timeprofile to produce substantially the same result as long as the samplesdo not all coincide with zero crossings. Furthermore, it is notnecessary that the sampling be done at a constant rate. Although severalexamples provided herein involve samples equally spaced apart in time,sampling of the time profile can be done with unequal time spacingbetween samples. Additionally, one skilled in the art will recognizethat the samples in FIG. 13 are relative to a 0.0 v reference chosen tosimplify the example prototype signals provided herein and willunderstand that a 0.0 v reference is not a requirement of the invention.

FIG. 14 depicts the samples 130 of FIG. 13 without the prototype signal30. Depending on the sampling rate and the alignment of the samples 130to the prototype signal 30, the silhouette, or outline, of the samples130 may be substantially similar to the shape of the envelope of theprototype signal 30 or may otherwise resemble the prototype signal 30.In FIG. 14, for example, the silhouette of the samples 130 appears to bethe same as the shape of the envelope of the prototype signal 30.However, it is not necessary for the silhouette of the samples to be thesame as the shape of the envelope or otherwise resemble the prototypesignal 30 to practice the invention. In FIG. 15, for example, theprototype signal 30 of FIG. 3 is also shown being sampled at the 8 GHzrate, but the samples 150 are shifted so they no longer coincide withthe crests 132 of the prototype signal 30. FIG. 16 shows the samples 150of FIG. 15 without the prototype signal 30. In FIG. 16, it is apparentthat the silhouette of the samples 150 has the same duration as thesilhouette of the samples 130 in FIG. 14. It is also apparent that thesilhouette of the samples 150 is not the same as the shape of theenvelope of the prototype signal 30.

To practice the invention, it is not necessary to sample the prototypesignal at the Nyquist rate. In an alternative embodiment, the prototypesignal is sampled at a rate that is less than the Nyquist rate. In otherwords, the prototype signal is sampled at a rate that is less than twiceits carrier frequency. FIG. 17 depicts the prototype signal 30 of FIG. 3being sampled at 5 GHz. The samples 170 are aligned so as to coincidewith every eighth crest 132, although such alignment is arbitrary. FIG.18 shows the samples 170 of FIG. 17 without the prototype signal 30. Inanother alternative embodiment, the prototype signal is sampled at arate that is greater than the Nyquist rate. In other words, theprototype signal is sampled at a rate that is more than twice itscarrier frequency. FIG. 19 shows the prototype signal 30 of FIG. 3 beingsampled at 10 GHz. The samples 190 are aligned so as to coincide withevery fourth crest 132, although such alignment is arbitrary. FIG. 20shows the samples 190 of FIG. 19 without the prototype signal 30.

Thus, in accordance with the invention, the prototype signal can besampled at different rates and with different sample alignments.

Generated RF Waveforms

Under the present invention, a plurality of RF waveforms is generated inaccordance with the polarity, timing, and magnitude of correspondingsamples of the time profile. An RF waveform generated in accordance withone embodiment of the present invention can be an impulse, doublet,triplet, gaussian, step, triangle, sawtooth, burst of cycles, or anyother suitable type of RF waveform having an instantaneous bandwidththat is greater than or equal to the instantaneous bandwidth of theprototype signal and having an average bandwidth that is greater than orequal to the average bandwidth of the prototype signal. In a furtherembodiment, each of the plurality of RF waveforms is the same type asthe other RF waveforms. For example, all of the RF waveforms could beimpulses. In an alternative embodiment, the plurality of RF waveformsincludes two or more different types of RF waveforms. For example, theplurality of RF waveforms could include a combination of doublets andtriplets or the plurality of RF waveforms could involve bursts havingdifferent numbers of cycles.

Polarity of the RF Waveforms

In accordance with the invention, the polarity of each generated RFwaveform of the plurality of RF waveforms is in accordance with thepolarity of a corresponding sample of the prototype signal. In oneembodiment, the polarity of each generated RF waveform of the pluralityof RF waveforms is the same as the polarity of a corresponding sample ofthe prototype signal. In an alternative embodiment, the polarity ofselected generated RF waveforms is opposite the polarity ofcorresponding samples of the prototype signal.

Relative Timing of the RF Waveforms

In accordance with the invention, the timing of the RF waveformscorresponds to the timing of the samples of the time profile. Like thesamples of the time profile, the time spacing between the generated RFwaveforms can be equal (or substantially equal) or unequal. In otherwords, the generated RF waveforms may be equally (or substantiallyequally) spaced in time or unequally spaced in time. Generally, whetherthe RF waveforms are equally or unequally spaced in time depends onwhether the samples are equally or unequally spaced.

In one embodiment, the relative timing of the plurality of the RFwaveforms is equal to the relative timing of the samples of the timeprofile of the prototype signal. Under this arrangement, the timespacing between a given RF waveform and the following RF waveform is thesame (or substantially the same) as the time spacing between the twosamples corresponding to those RF waveforms. In an alternate embodiment,the timing of RF waveforms is based upon by somewhat different than thetiming of the samples. Under this arrangement, the timing of the samplesof the prototype signal corresponds to the nominal time positioning ofthe generated RF waveforms but the actual time positions of thegenerated RF waveforms are dithered, or otherwise shifted, relative tothe nominal time positions. By dithering the actual time positions ofthe generated RF waveforms, higher harmonics may be suppressed thatmight otherwise be present in the frequency profile of RF waveformsdepending on the rate at which the time profile of the prototype signalis sampled. Further discussion of the relationship of harmonics to therate of sampling of the time profile of the prototype signal is providedbelow. In a further embodiment, the dithering of the time positions ofthe generated RF waveforms is performed pseudorandomly. In still anotherembodiment, the dithering of the time positions of the generated RFwaveforms is in accordance with a code. In another exemplary embodimentof the present invention, the timing of the plurality of RF waveformsmay be programmable.

In one embodiment, the relative time positions of the generated RFwaveforms correspond to the zero crossings of the generated RFwaveforms. In another embodiment, the relative time positions of thegenerated RF waveforms correspond to the crests of the generated RFwaveforms. For example, in doublet pulses, the timing of the pluralityof RF waveforms can correspond to a zero crossing or a crest of each RFwaveform. Alternatively, the timing of the plurality of RF waveforms cancorrespond to an arbitrarily selected location of each RF waveform, forexample, the beginning of each RF waveform. As such, the time spacingbetween the generated RF waveforms corresponds to the time spacingbetween the samples of the time profile.

The timing of the plurality of RF waveforms can define the centerfrequency of main lobes present in the frequency profile of thegenerated plurality of RF waveforms, where the frequency profile has aplurality of main lobes corresponding to a fundamental spectra,harmonics of the fundamental spectra, and possibly fold images of thefundamental spectra and harmonics that may or may not exist depending onthe rate at which the RF waveforms are generated. One skilled in the artwill recognize that one or more of these main lobes may or may notreside within the frequency band of interest depending on the selectedgeneration rate and the selected frequency band of interest. As such,the timing of the plurality of RF waveforms may correspond to a desiredcenter frequency within the frequency band of interest. Furtherdiscussion of the generation rate, fundamental spectra, harmonics, andfold images is provided below.

Scaling of the RF Waveforms

In accordance with the invention, the energy contained in each generatedRF waveform of the plurality of RF waveforms is scaled in accordancewith a corresponding sample of the prototype signal to produce aggregateRF energy having spectral characteristics substantially similar to, oremulating, those of the desired waveform.

Scaling, in accordance with the present invention, is to pattern, make,set, regulate, or estimate the energy of each RF waveform of theplurality of RF waveforms according to a corresponding sample value ofthe plurality of sample values relative to a reference value. In oneembodiment, the reference value corresponds to the maximum sample value.In an alternative embodiment, the reference value is the maximum valueof the time profile of the prototype signal. As previously shown, themaximum sample value may or may not equal the maximum value of the timeprofile depending on the alignment of the samples.

In accordance with the invention, the energy of each RF waveform of theplurality of RF waveforms is scaled by varying at least one ofamplitude, width or waveform type based on the value of a correspondingone of the plurality of samples relative to a reference value. In oneembodiment, each RF waveform of the plurality of RF waveforms can havesubstantially the same width, with the amplitude of each RF waveformbeing determined based on the value of a corresponding one of theplurality of sample values relative to the reference value. In analternative embodiment, each of the plurality of RF waveforms can havesubstantially the same amplitude, with their widths being determinedbased on the value of a corresponding one of the plurality of samplevalues relative to the reference value. In another alternativeembodiment, the widths and amplitudes of each of the plurality of RFwaveforms can be varied to scale the energy of the RF waveforms. In afurther embodiment, both the width and amplitude are varied such that adefined amplitude/width ratio is maintained for each RF waveform of theplurality of RF waveforms. In still another embodiment, the waveformtype, or shape, of each RF waveform can be varied in order to achievethe appropriate energy scaling. For example, the number of cycles in RFwaveforms comprising bursts of cycles can be varied.

The sample values depicted in FIG. 13 and FIG. 14 correspond to thescaling factors listed in Table. 1.

TABLE 1 1. 1. 0.000 2. 2. −0.096 3. 3. 0.193 4. 4. −0.288 5. 5. 0.381 6.6. −0.469 7. 7. 0.554 8. 8. −0.632 9. 9. 0.704 10. 10. −0.770 11. 0.82912. −0.879 13. 0.922 14. −0.955 15. 0.979 16. −0.993 17. 1.000 18.−0.993 19. 0.979 20. −0.955 21. 0.922 22. −0.879 23. 0.829 24. −0.77025. 0.704 26. −0.632 27. 0.554 28. −0.469 29. 0.381 30. −0.288 31. 0.19332. −0.096 33. 0.000

When generating the plurality of RF waveforms in accordance with thesamples of Table 1, the 17^(th) RF waveform corresponds to the referencevalue. Therefore, the 17^(th) RF waveform has some predetermined maximumamount of energy and the other RF waveforms are scaled relative to it.The 3^(rd) RF waveform, for example, would have 19.3% of the energy ofthe 17^(th) RF waveform. Thus, in accordance with the invention, aplurality of generated RF waveforms spaced apart by 0.125 ns and havingpolarity and scaled energy based on the samples of Table 1 produceaggregate energy substantially similar to and thereby emulating theenergy of the prototype signal and thus the desired waveform. Oneskilled in the art will recognize that the prototype signal of FIG. 13has 33 samples aligned with the crests resulting in the first and lastsamples being zero thereby eliminating the first RF waveform and last RFwaveform. In accordance with the invention, samples could be aligneddifferently to prevent elimination of the first and last RF waveforms.In particular, the first and last samples could be shifted as requiredto achieve non-zero sample values. Alternatively, samples can bepurposely aligned to coincide with an optimal number of zero crossings(or near zero crossings) so as to minimize the number of generated RFwaveforms and thereby reduce the costs of defining and generating them(i.e., memory requirements, power requirements, etc.).

In one embodiment of the invention, the RMS amplitudes and polarities ofthe generated RF waveforms are scaled in accordance with sample valuesof the time profile of the desired signal. The RMS amplitudes of the RFwaveforms can be scaled by varying or otherwise modulating theamplitudes of the RF waveforms, the widths of the RF waveforms, thetypes of the RF waveforms, or some combination thereof based on thevalue of a corresponding one of the plurality of sample values relativeto a reference value. The reference value can correspond to the maximumvalue of the plurality of sample values and can correspond to themaximum value of the time profile. In Table 1, for example, the maximumvalue corresponds to sample value 17. The sample values can benormalized for signal processing in accordance with the presentinvention.

Each RF waveform of the plurality of RF waveforms can have substantiallythe same width, with the amplitude of each RF waveform being determinedbased on the value of a corresponding one of the plurality of samplevalues relative to the maximum value. In an alternative embodiment, eachof the plurality of RF waveforms can have substantially the sameamplitude, with their widths being determined based on the value of acorresponding one of the plurality of sample values relative to themaximum value. Both the width and amplitude can be determined such thata defined amplitude/width ratio is maintained for each RF waveform ofthe plurality of RF waveforms. The waveform type, or shape, of each RFwaveform can be varied in order to achieve the appropriate energyscaling. For example, the number of cycles in RF waveforms comprisingbursts of cycles can be varied. The present invention can also usewaveforms of different shapes having different RMS amplitudes.

In an exemplary embodiment, generated RF waveforms are impulses havingamplitudes scaled in accordance with the invention, which could bedepicted in the same manner as the samples shown in FIGS. 13 through 20.FIGS. 21 through 24 compare the frequency profiles of impulses generatedbased on the samples of FIGS. 13, 15, 17, and 19, respectively, to thefrequency profile 40 shown in FIG. 4 of the prototype signal 30 of FIG.3.

FIG. 21 overlays the frequency profile 40 of FIG. 4 and the frequencyprofile 210 of impulses generated based on the samples 130 of FIG. 13.In FIG. 21, it is evident that the frequency profile 210 of the impulsesis substantially similar to the frequency profile 40 of the prototypesignal 30. In particular, the main lobe 214 of frequency profile 210appears to be about the same as the main lobe 44 of frequency profile40, especially within the frequency band of interest 10.

FIG. 22 overlays the frequency profile 40 of FIG. 4 and the frequencyprofile 220 of impulses generated based on the samples 150 of FIG. 15.As previously described, the samples 150 of FIG. 15 have the sameNyquist sampling rate of the samples 130 of FIG. 13 except they havebeen shifted off the crests 132. In FIG. 22, it is evident that thefrequency profile 220 of the impulses is substantially similar to thefrequency profile 40 of the prototype signal 30. In particular, the mainlobe 224 of frequency profile 220 appears to be about the same as themain lobe 44 of frequency profile 40, especially within the frequencyband of interest 10.

FIG. 23 overlays the frequency profile 40 of FIG. 4 and the frequencyprofile 230 of impulses generated based on the samples 170 of FIG. 17.As previously described, the samples 170 of FIG. 17 have a sampling ratethat is less than the Nyquist rate, specifically 5 GHz. In FIG. 23, itis evident that the frequency profile 230 of the impulses issubstantially similar to the frequency profile 40 of the prototypesignal 30. In particular, the main lobe 234 of frequency profile 230appears to be about the same as the main lobe 44 of frequency profile40, especially within the frequency band of interest 10.

FIG. 24 overlays the frequency profile 40 of FIG. 4 and the frequencyprofile 240 of impulses generated based on the samples 190 of FIG. 19.As previously described, the samples 190 of FIG. 19 have a sampling ratethat is greater than the Nyquist rate, specifically 10 GHz. In FIG. 24,it is evident that the frequency profile 240 of the impulses issubstantially similar to the frequency profile 40 of the prototypesignal 30. In particular, the main lobe 244 of frequency profile 240appears to be about the same as the main lobe 44 of frequency profile40, especially within the frequency band of interest 10.

Thus, FIGS. 21 through 24 provide four examples of a plurality ofimpulses generated based on samples of the prototype signal 30 of FIG. 3emulating the prototype signal 30 such that the frequency profile of theimpulses is substantially similar to the frequency profile 40 of theprototype signal 30. Furthermore, FIGS. 21 through 24 also provide fourexamples of a plurality of impulses generated based on samples of theprototype signal 30 of FIG. 3 emulating the desired waveform comprisingthe main lobe 20 of FIG. 2, where the spectral characteristics of theplurality of impulses substantially meet desired spectral requirements

FIGS. 25 through 34 present examples of alternative RF waveformsgenerated in accordance with the invention having constant widths andamplitudes scaled based on the same plurality of samples of the timeprofile of the prototype signal 30 of FIG. 3. For clarity, the timeprofile of the prototype signal is sampled at 2 GHz for these examplesto space the RF waveforms sufficiently apart so that they don't overlap,which one skilled in the art will understand can occur for non-impulseRF waveforms depending on the spacing of the samples and the width ofthe RF waveforms.

FIG. 25 depicts impulses 250 scaled in accordance with samples of thetime profile of the prototype signal 30 of FIG. 3. For additionalclarity, the prototype signal 30 is not shown, nor the sampling of it.Instead, markers 252 denote the time locations of the samples. FIG. 26illustrates the frequency profile 260 of the impulses overlaid upon thefrequency profile 40 of the prototype signal 30 of FIG. 3. It is evidentthat the frequency profile 260 of the impulses is substantially similarto the frequency profile 40 of the prototype signal 30. In particular,the main lobe 264 of frequency profile 260 appears to be about the sameas the main lobe 44 of frequency profile 40, especially within thefrequency band of interest 10.

FIG. 27 depicts doublets 270 scaled in accordance with samples of thetime profile of the prototype signal 30 of FIG. 3. Markers 252 denotethe time locations of the samples. In FIG. 27, the location of thedoublets 270 was arbitrarily selected such that a point to the left oftheir first (positive lobe) coincides with the time of each sample. Asexplained earlier, the doublets could be shifted such that the sampletimes coincide with their crests, zero crossings, or some otherarbitrary selected location. FIG. 28 illustrates the frequency profile280 of the doublets overlaid upon the frequency profile 40 of theprototype signal 30 of FIG. 3. As is the case with the previous examplesinvolving impulses, it is evident that the frequency profile 280 of thedoublets is substantially similar to the frequency profile 40 of theprototype signal 30. In particular, the main lobe 284 of frequencyprofile 280 appears to be about the same as the main lobe 44 offrequency profile 40, especially within the frequency band of interest10.

FIG. 29 depicts triplets 290 scaled in accordance with samples of thetime profile of the prototype signal 30 of FIG. 3. In FIG. 29, thelocation of the triplets 290 was arbitrarily selected such that mainlobe of the triplets aligns with the sample times. FIG. 30 illustratesthe frequency profile 300 of the triplets overlaid upon the frequencyprofile 40 of the prototype signal 30 of FIG. 3. Again, markers 252indicate the time locations of the samples. It is evident that thefrequency profile 300 of the triplets is substantially similar to thefrequency profile 40 of the prototype signal 30. In particular, the mainlobe 304 of frequency profile 300 appears to be about the same as themain lobe 44 of frequency profile 40, especially within the frequencyband of interest 10.

FIG. 31 depicts Gaussian pulses 310 scaled in accordance with samples ofthe time profile of the prototype signal 30 of FIG. 3. In FIG. 31, thelocation of the Gaussian pulses 310 was arbitrarily selected such thatthe pulses are centered about the sample times. FIG. 32 illustrates thefrequency profile 320 of the Gaussian pulses overlaid upon the frequencyprofile 40 of the prototype signal 30 of FIG. 3. Again, markers 252indicate the time locations of the samples. It is evident that thefrequency profile 320 of the Gaussian pulses is substantially similar tothe frequency profile 40 of the prototype signal 30. In particular, themain lobe 324 of frequency profile 320 appears to be about the same asthe main lobe 44 of frequency profile 40, especially within thefrequency band of interest 10.

FIG. 33 depicts triangle waveforms 330 scaled in accordance with samplesof the time profile of the prototype signal 30 of FIG. 3. In FIG. 33,the location of the triangle waveforms 330 was arbitrarily selected suchthat the triangle waveforms are centered about the sample times. FIG. 34illustrates the frequency profile 340 of the triangle waveforms overlaidupon the frequency profile 40 of the prototype signal 30 of FIG. 3.Again, markers 252 indicate the time locations of the samples. It isevident that the frequency profile 340 of the triangle waveforms issubstantially similar to the frequency profile 40 of the prototypesignal 30. In particular, the main lobe 344 of frequency profile 340appears to be about the same as the main lobe 44 of frequency profile40, especially within the frequency band of interest 10.

Thus, FIGS. 25 through 34 provide examples of a pluralities of impulse,doublet, triplet, Gaussian, and triangle waveforms respectively,generated based on samples of the prototype signal 30 of FIG. 3emulating the prototype signal 30 such that their frequency profiles aresubstantially similar to the frequency profile 40 of the prototypesignal 30. Furthermore, FIGS. 25 through 34 also provide examples of apluralities of impulse, doublet, triplet, Gaussian, and trianglewaveforms respectively, generated based on samples of the prototypesignal 30 of FIG. 3 emulating the desired waveform comprising the mainlobe 20 of FIG. 2, where the spectral characteristics of the various RFwaveforms substantially meet desired spectral requirements.

By comparing FIGS. 26, 28, 30, 32, and 34 it is apparent that theexample frequency profiles of the pluralities of impulse, doublet,triplet, Gaussian, and triangle waveforms generated in accordance withthe invention are substantially the same, especially within thefrequency band of interest 10.

As discussed previously, under one embodiment of the invention, theamplitude of each generated RF waveform of the plurality of RF waveformsis held constant (or substantially constant) and the widths of the RFwaveforms are scaled based on corresponding samples of the prototypesignal. FIG. 35 presents square wave pulses 350 having the sameamplitude and having widths scaled in accordance with the samples shownin FIGS. 13 and 14. In FIG. 35, the location of the square wave pulses350 was arbitrarily selected such that the pulses are centered about thesample times. FIG. 36 illustrates the frequency profile 360 of thesquare wave pulses overlaid upon the frequency profile 40 of theprototype signal 30 of FIG. 3. Again, markers 252 indicate the timelocations of the samples. It is evident that the frequency profile 360of the square wave pulses is substantially similar to the frequencyprofile 40 of the prototype signal 30. In particular, the main lobe 364of frequency profile 360 appears to be about the same as the main lobe44 of frequency profile 40, especially within the frequency band ofinterest 10.

In accordance with the invention, the amplitudes of the other types ofRF waveforms can also be held constant (or substantially constant) andtheir widths varied to scale their energy based on samples of the timeprofile of the prototype signal. Furthermore, one skilled in the artwill recognize that the energy of any one RF waveform of the pluralityof RF waveforms can be scaled by varying the amplitude or width or boththe amplitude and width. In other words, the amplitude and width of anyRF waveform of the plurality of RF waveforms can be allowed to vary.Additionally, when amplitudes and widths are allowed to vary, a constant(or substantially constant) ratio of amplitude to width can bemaintained such that the waveforms have the same general appearance butare scaled proportionally.

Filtering

In one embodiment of the invention, the aggregate energy spectra of theplurality of RF waveforms can optionally be limited to the frequencyband of interest or to some other frequency band. One skilled in the artwill recognize that a lowpass filter, highpass filter, bandpass filter,or a combination of a lowpass filter and a highpass filter can be usedto remove frequencies below and/or above a frequency band of interest.FIG. 37, for example, depicts the frequency profile 210 of impulsesgenerated based on the samples 130 of FIG. 13 overlaid on the frequencyprofile 40 of the prototype signal 30 as previously shown in FIG. 21,except FIG. 37 is ‘zoomed out’ to show frequencies from 0 to 10 GHz. InFIG. 37, a larger frequency band of interest than the one previouslyshown has been selected, which is from 3 to 5 GHz. One skilled in theart will recognize that the frequency profile 210 of the plurality ofimpulses generated in accordance with the invention includes lowfrequency and high frequency spectral artifacts not present in frequencyprofile 40 of the prototype signal 30. These ‘out of band’ spectralartifacts that can be produced in accordance with the invention may ormay not be significant. For certain applications of the invention, suchspectral artifacts may simply be ignored while in other applications itmay be desirable to filter out the spectral artifacts. Accordingly, inan optional embodiment of the invention, such spectral artifacts can befiltered using conventional filtering techniques.

FIG. 38 presents the time profile of a filtered waveform 380 produced bybandpass filtering out of band spectral artifacts of the aggregateenergy of the plurality of impulses generated in accordance with theinvention, where the time profile of the filtered waveform 380 isoverlaid upon the time profile of the prototype signal 30. From FIG. 38it is evident that the filtered waveform 380 is substantially the sameas the prototype signal 30.

One skilled in the art will also understand that electronic componentscan be selected that do not respond to certain low and/or highfrequencies and therefore effectively filter them in a manner similar toa filter device.

RF Waveform Generator

According to another aspect of the invention, a method for generatingwaveforms includes generating the plurality of RF waveforms at awaveform generation rate that is selected in accordance with a centerfrequency within a frequency band of interest. Each RF waveform of theplurality of RF waveforms is modulated in accordance with the timeprofile of the desired waveform to produce an aggregate RF energy thatapproximates the spectral characteristics of the desired waveform. Theplurality of RF waveforms can be amplitude and/or width modulated inaccordance with the sample values of the time profile to produce thedesired aggregate RF energy.

FIG. 39 shows a block diagram of a waveform generator 390 in accordancewith one embodiment of the present invention. In its simplest form, thewaveform generator 390 of the invention generates a plurality of RFwaveforms in accordance with samples of the prototype signal to produceaggregate energy with a desired PSD within a frequency band of interest,e.g., 3 GHz to 5 GHz.

In accordance with one embodiment, the timing between each of theplurality of RF waveforms is substantially the same. The waveformgenerator 390 of the present invention includes an oscillator 392, atimer 394 that generate the plurality of RF waveforms at a waveformgeneration rate. Under one embodiment, the waveform generator 390 has avariable rate controlled by a variable timer 394, which may beprogrammable for setting the time spacing between RF waveforms, therebychanging the center frequency of the generated waveform. In accordancewith an alternative embodiment, the variable timer 394 can also be usedto produce RF waveforms having non-uniform time spacing.

The waveform generator 390 includes an envelope modulator 396 thatamplitude modulates the generated plurality of RF waveforms inaccordance with sample values of a time profile of a prototype signalhaving a desired envelope. Thus, the waveform generator 390 generates aplurality of RF waveforms each having energy scaled in accordance withthe invention to produce aggregate energy that emulates the prototypesignal and thus the desired waveform. As explained above, amplitude,width or a combination of both can be varied to scale the energy of theRF waveforms. Accordingly, envelope modulator 396 of FIG. 39 canalternatively be replaced by a width modulator or a modulator capable ofvarying both the width and amplitude of the RF waveforms in accordancewith the present invention.

In accordance with one embodiment, the duration, shape and peakamplitude of the desired envelope can be programmable so as to vary theemulated prototype signal for data modulation and/or channelizationpurposes. The modulator can include an input for modulating the RFwaveforms and/or an input for defining a communications channel. Theplurality of RF waveforms and thus the emulated prototype signal may bemodulated using various modulation techniques including, but not limitedto, single or multi-level phase modulation (e.g., BPSK, QPSK, QAM, etc)as well as any differential variations thereof, e.g., DBPSK. Thus, thedesired waveform can also be modulated by an information signal or inaccordance with a code.

In FIG. 39, the envelope modulator 396 is shown to have an optional datamodulation signal input that might cause it to affect the samples issome manner as to convey information. A ‘channel code’ signal could alsobe applied to the envelope modulator 396 in conjunction with or as analternative to the data modulation signal. Alternatively, the optionaldata modulation signal and/or channel code signal could be input intothe timer in order to affect the timing of the RF waveforms in somemanner as to convey information and/or for channelization purposes. Thedata modulation and/or channel code signal could also be applied to boththe envelope modulator 396 and the programmable timer 394. One skilledin the art will recognize that various methods could be applied toaffect the plurality of RF waveforms as to convey information and/or todefine a communications channel.

FIG. 39 also includes an optional filter 398 that limits the aggregateenergy of the plurality of RF waveforms to the frequency band ofinterest. In the exemplary embodiment, filter 398 limits the aggregateenergy of the plurality of RF waveforms to the exemplary frequency bandof interest in the 3 GHz to 5 GHz range. As described below, filter 398can also be used to select any harmonic of the plurality of harmonics inthe spectra of the aggregate energy of the plurality of RF waveforms,which may exist depending on the waveform generation rate. In analternative embodiment, each of the RF waveforms can be individuallyfiltered as they are generated.

In the embodiment shown in FIG. 39, an oscillator 392 and programmabletime 394 are used to establish the waveform generation rate, thereby thetiming or time spacing between the RF waveforms. The timing correspondsto the center frequency of the main lobes of the aggregate energy of theRF waveforms. Under the exemplary embodiment shown in FIG. 39,oscillator 392 and programmable time 394 generate a plurality ofconstant amplitude RF waveforms, and an amplitude modulator 396modulates such signals to produce the plurality of RF waveforms scaledin accordance with the invention. In another embodiment, each signal ofthe plurality of variable amplitude (or width) RF waveforms is digitallyrepresented in terms of quantized amplitude (or width) representations.The quantized values correspond to the amplitude (or width) of each ofthe plurality of RF waveforms. Such quantized values can be stored in amemory (not shown). The stored quantized representations can then beretrieved and applied to a digital to analog converter (DAC) and inputinto the envelope modulator 396 to generate the RF waveforms at ageneration rate defined by the oscillator 392 and time 394. Aspreviously described, each RF waveform can be a wideband signal,including impulses, doublets, triplets, gaussian, or any other suitabletype of waveform. Thus, the envelope modulator can include circuitryrequired to produce a desired shape of the RF waveforms (e.g., a doubletshape). Thus, each of the plurality of RF waveforms can be separatelygenerated as one of a plurality of digital waveforms or a plurality ofanalog waveforms. The plurality of analog waveforms can be generated inresponse to one or more digital signals of a plurality of digitalsignals that are stored in a memory.

The Nyquist Theorem

The Nyquist Theorem, also known as the sampling theorem, is a principlethat relates to digitization of waveforms. The theorem, developed by H.Nyquist, states that an analog signal waveform may be uniquelyreconstructed, without error, from samples taken at equal time intervalsat a sampling rate that is equal to or greater than twice the highestfrequency component in the waveform. According to the theorem, if awaveform is sampled at less than twice its highest frequency component,the reconstructed waveform effectively contributes only noise. Thisphenomenon is called “aliasing” (the high frequencies are “under analias”). For example, according to the Nyquist Theorem, the faithfulreproduction of a 4 GHz waveform requires a sampling rate equal to orgreater than 8 GHz. Similarly, for faithful reproduction of a 5 GHzwaveform, the Nyquist Theorem requires a sampling rate equal to orgreater than 10 GHz. In practice, however, the sampling rate used todigitize waveforms is often set to 2.5 times the highest frequency.

Fundamental Spectra, Harmonics, and Fold Images

As previously described, the time profile of the prototype signal can besampled in accordance with the invention at the Nyquist sampling rate orat a rate less than or greater than the Nyquist rate. A plurality of RFwaveforms are then scaled in accordance with corresponding samples ofthe time profile of the prototype signal to produce aggregate energyemulating that of the prototype signal where the timing of the RFwaveforms corresponds to the timing of the samples. Thus, the waveformgeneration rate corresponds to the sampling rate.

The sampling rate and corresponding RF waveform generation rate used inaccordance with the invention determines characteristics of theaggregate energy of the generated plurality of RF waveforms. Aspreviously described, the carrier frequency of the prototype signaldetermines the center frequency of the fundamental spectra, and theenvelope width and shape determines the bandwidth of the fundamentalspectra. The sample/waveform generation rate determines the location ofharmonics of the fundamental spectra relative to the center frequency ofthe fundamental spectra where each harmonic has the same bandwidth asthe fundamental spectra. Specifically, harmonics of the fundamentalspectra occur at even intervals of the generation rate relative to thecenter frequency of the fundamental spectra. For example, for aprototype signal having a 3.5 GHz carrier, the center frequency of thefundamental spectra of the plurality of RF waveforms generated inaccordance with the invention is 3.5 GHz. If the prototype is sampled at7 GHz and the plurality of RF waveforms generated at 7 GHz, harmonics ofthe fundamental spectra will occur at 10.5 GHz, 17.5 GHz, 24.5 GHz,etc., which corresponds to 3.5 GHz±N×7 GHz. FIG. 40 depicts the spectraof the prototype signal 400, the fundamental spectra 402 having a centerfrequency 404 of 3.5 GHz, and a harmonic 406 of the fundamental spectra402 having a center frequency 408 at 10.5 GHz.

When the center frequency of the fundamental spectra is not a multipleof the sample/generation rate or vice versa, fold images will existhaving fold frequencies at even multiples of the sample/generation rate.For example, in FIG. 41, the prototype signal 410 has a 3.5 carrierfrequency and is sampled at 3 GHz. The alignment of the samples 412 wasarbitrarily selected. FIG. 42 depicts the frequency profile of theplurality of RF waveforms generated in accordance with the samples ofFIG. 41 overlaid upon the frequency profile 420 of the prototype signal410. When impulses are scaled in accordance with the samples 412, thefrequency profile of the plurality of RF waveforms shown in FIG. 42includes fundamental spectra 421 with a center frequency of 3.5 GHz;harmonics 422 of the fundamental spectra 421 at 0.5 GHz, 6.5 GHz, 9.5GHz, 12.5 GHz, 15.5 GHz, etc.; fold frequencies at 0 GHz, 3.0 GHz, 6.0GHz, 9.0 GHz, 12.0 GHz, 15.0 GHz, etc.; and fold images 424 mirroringthe fundamental spectra 421 and harmonics 422 that are centered atfrequencies on the opposite side of the fold frequencies. Specifically,fold images 424 occur at 2.5 GHz, 5.5 GHz, 8.5 GHz, 11.5 GHz, 14.5 GHz,etc. FIG. 42 also shows a frequency band of interest 426 spanning from 3GHz to 5 GHz.

As previously described, filtering can be used to remove out of bandspectral artifacts. Referring again to FIG. 42, it is evident that theharmonics 422 and fold images 424 reside outside the frequency band ofinterest 426, which contains the fundamental spectra 421. FIG. 43presents the filtered waveform 430 produced by using one or more filtersto remove out of band frequencies from the aggregate energy spectra ofthe generated plurality of RF waveforms. In FIG. 43, filtered waveform430 is substantially similar to the prototype signal 410 of FIG. 41.Thus, one or more filters may be used to limit the spectral energy ofthe plurality of RF waveforms to within a frequency band of interest.

Generally, one skilled in the art will recognize that one or morefilters can be used to limit the spectral energy of the plurality of RFwaveforms to one or more of the fundamental spectra, harmonics, and foldimages. The one or more of the fundamental spectra, harmonics, and foldimages can be selected in accordance with a code, which defines acommunications channel, and can be selected in accordance with aninformation signal as a form of modulation.

In FIG. 44, the sample/generation rate used in the example of FIG. 41has been changed from 3.0 GHz to 4.0 GHz. Thus, the prototype signal410, which has a carrier frequency of 3.5 GHz, is now sampled at 4.0GHz. The alignment of the samples 440 was arbitrarily selected. FIG. 45depicts the frequency profile of the plurality of RF waveforms generatedin accordance with the samples of FIG. 44 overlaid upon the frequencyprofile 420 of the prototype signal 410. When impulses are scaled inaccordance with the samples 440, the frequency profile includesfundamental spectra 451 with a center frequency of 3.5 GHz and harmonics452 of the fundamental spectra at 7.5 GHz, 11.5 GHz, 15.5 GHz, 19.5 GHz,etc.; fold frequencies at 0 GHz, 4.0 GHz, 8.0 GHz, 12.0 GHz, 16.0 GHz,20.0 GHz, etc.; and fold images 454 mirroring the fundamental spectra451 and harmonics 452 at frequencies that are on the opposite side ofthe fold frequencies. Specifically, fold images 454 occur at 0.5 GHz,4.5 GHz, 8.5 GHz, 12.5 GHz, 16.5 GHz, etc. FIG. 45 also shows thefrequency band of interest 426 spanning from 3 GHz to 5 GHz. Thus, it isapparent that using a filter to remove out of band frequencies will notremove the fold image 454 corresponding to the fundamental spectra 451since it resides within the frequency band of interest 426. FIG. 46presents the filtered waveform 460 produced by using one or more filtersto remove out of band frequencies from the aggregate energy spectra ofthe generated plurality of RF waveforms. In FIG. 46, filtered waveform460 is substantially different than the prototype signal 410 of FIG. 44because of the fold image remaining within the frequency band ofinterest. One skilled in the art will recognize that if filtering werethe only available means for removing undesirable spectralcharacteristics that a different prototype carrier frequency orsampling/generation rate might be used to cause the fold image to nolonger reside within the frequency band of interest. An alternativemeans for removing fold images is provided below.

Group Sampling and RF Waveform Generation

In accordance with the invention, RF waveforms may be scaled andgenerated in one or more groups to eliminate a fold image. In oneembodiment of the invention, the prototype signal is sampled and RFwaveforms are generated in one or more groups, with each groupcomprising two or more RF waveforms having a predefined time spacing. Inan exemplary embodiment, each group consists of a pair of RF waveformshaving predefined time spacing corresponding to one fourth of the periodof the fold frequency of a fold image to be eliminated. The inventorsrefer to the first pulse of each pulse pair as the I pulse and thesecond pulse of each pair as the Q pulse. For example, pairs of RFwaveforms can be used to eliminate the fold image 454 residing withinthe frequency band of interest 426 of FIG. 45, which has a foldfrequency of 4 GHz. As shown in FIG. 47, each of the samples 440 of theprototype signal 410, as previously shown in FIG. 44, is paired withanother sample 470. The samples of each pair are spaced apart in time byone fourth of the period of the 4 GHz fold frequency of the fold imageto eliminate, or 0.0625 ns. Markers 252 corresponding to the firstsample of each sample pair and markers 472 corresponding to the secondsample of each sample pair indicate the timing of the sample pairs.

FIG. 48 depicts the frequency profile 420 of the prototype signal 410overlaid upon the frequency profile of a plurality of RF waveformsgenerated in accordance with the group sampling method of the invention.When comparing FIG. 48 to FIG. 45, it is evident that the fundamentalspectra 451 remains within the frequency band of interest 426 and issubstantially similar to the frequency profile of the prototype signal420. The first harmonic 452 of the desired waveform 451 remains as wellas the first and third fold images 454. However, the fold image 454,which had resided within the frequency band of interest 426 in FIG. 45,is no longer present in FIG. 48. FIG. 49 presents the filtered waveform490 produced by using one or more filters to remove out of bandfrequencies from the aggregate energy spectra of the generated pluralityof RF waveforms. In FIG. 49, filtered waveform 490 is substantiallysimilar to the prototype signal 410 of FIG. 47.

In accordance with the invention, the fold image having a fold frequencyof 8 GHz can be eliminated by changing the time spacing between samplesto one fourth of the period of the 8 GHz fold frequency of the foldimage to eliminate, or 0.0375 ns, and so forth. Furthermore, groups oftwo or more samples having a predefined time spacing (and correspondingRF waveforms) can also be used in accordance with the invention toeliminate fold images.

FIG. 50 shows a block diagram for implementing this aspect of thepresent invention. FIG. 50 includes first and second RF waveformgenerators, 5002 and 5004, respectively, that together generate pairs ofRF waveforms in accordance with pairs of samples of the prototypesignal. The first RF waveform generator 5002 generates a first pluralityof RF waveforms in accordance with the first sample of each pair ofsamples of the prototype signal, and the second RF waveform generator5004 generates a second plurality of RF waveforms in accordance with thesecond sample of each pair of samples of the prototype signal. Underthis arrangement, a fixed rate oscillator 5005 corresponds to thewaveform generation rate of both the first plurality of RF waveforms andsecond plurality of RF waveforms. As shown, the second RF waveformgenerator 5004 includes a delay element 5006 that establishes the timespacing between each of the second plurality of RF waveforms and acorresponding one of the first plurality of RF waveforms. In otherwords, delay element 5006 establishes the time spacing between the RFwaveforms of each pair of RF waveforms. A combiner 5008 then combinesthe first plurality of RF waveforms and the second plurality of RFwaveforms into a combined plurality of RF waveforms. Finally, anoptional filter 5010 limits the spectral energy of the combinedplurality of RF waveforms to within a frequency band of interest.

In one embodiment, the first and second waveform generators amplitudemodulate their respective pluralities of RF waveforms. The first andsecond waveform generators 5002 and 5004 include corresponding first andsecond memories, 5016 and 5018, respectively, that store datarepresentative of quantized amplitudes of each RF waveform.Corresponding first and second digital-to-analog converters (DACs) 5012and 5014 convert the quantization data into analog signals used byimpulse generators to generate first and second pluralities of RFwaveforms.

As described previously, various methods can be used to modulate thecombined plurality of RF waveforms in order to convey information. Forexample, the first and second DACs, or the first and second impulsegenerators, could optionally include corresponding inputs for modulatingthe RF waveforms to convey information. Modulation methods include, butare not limited to, single or multi-level phase modulation (e.g., BPSK,QPSK, QAM, etc.) as well as any differential variations thereof, e.g.,DBPSK.

Of course, the impulse generators could be replaced with signalgenerators that generate other types of RF waveforms such as doublets,triplets, etc. It should be further noted that although this embodimentuses amplitude modulation, width modulation or a combination of bothmight also be used to scale the energy of the generated RF waveforms inaccordance with the pairs of samples of the prototype signal.

The RF waveform grouping method can be used to select between thefundamental spectra and its corresponding fold image. As shown in FIGS.47 through 49, samples having a time spacing of 0.0625 ns result inpairs of RF waveforms having energy spectra in which the fold imagewithin the frequency band of interest has been eliminated. The inventorshave determined that either the first RF waveform or the second RFwaveform of each pair of RF waveforms can be inverted to cause thefundamental spectra to be eliminated instead of its corresponding foldimage. This phenomenon can be seen in FIGS. 51 through 53. In FIG. 51,the prototype signal 410 is sampled in pairs where each pair comprises afirst sample 440 and a second sample 470. When comparing FIG. 51 to FIG.47 it can be seen that the second sample 470 of each pair has beeninverted, which results in the second RF waveform being inverted of eachRF waveform pair.

The frequency profile of the plurality of RF waveforms generated inaccordance with the samples of FIG. 51 is provided in FIG. 52. In FIG.52, it is apparent that the fold image 454 previously eliminated fromFIG. 48 is again present and instead the fundamental spectra 451 of FIG.48 has been eliminated. The same result occurs when the first RFwaveform of each RF waveform pair is inverted instead of the second RFwaveform.

FIG. 53 presents the filtered waveform produced by using one or morefilters to remove out of band frequencies from the aggregate energyspectra of the generated plurality of RF waveforms. In FIG. 53, filteredwaveform 530 has the same envelope shape as the prototype signal 410 ofFIG. 51 except the carrier frequency is now that of the fold imagepresent within the frequency band of interest. Thus, one skilled in theart will recognize that either the first or second RF waveform of eachpair of RF waveforms generated in accordance with the invention can beselectively inverted to toggle between emulation of a first prototypesignal having a first carrier frequency and a second prototype signalhaving a second carrier frequency.

The sample inverting technique can be useful for modulation,channelization, or other purposes. Another benefit of the technique isthat it can be used to lower system costs. For example, the techniquecould be used to produce a dual band communications system where onlythe sample pairs needed to define a signal transmitted in a first bandare stored in memory and the signal transmitted in a second band isdefined by inverted one of the samples of the stored sample pairs.Similarly, a multi-band communications system involving N bands coulduse the technique so only the samples that define N/2 bands are storedand the remaining bands are produced by inverting one of the samples ofeach stored pair of samples. Thus, system costs related to storage ofsample values in memory can be reduced. Use of the invention inMulti-band communications systems is discussed further below.

Additional Aspects of the Desired Waveform

Under one aspect of the invention, the desired waveform can correspondto a plurality of orthogonal waveforms. Thus, the time profile of thedesired waveform can correspond to the time profile of a plurality oforthogonal waveforms. In one embodiment, the desired waveformcorresponds to a plurality of orthogonal waveforms that are orthogonalwhen arriving at different times at a receiver. In another embodiment,the desired waveform corresponds to a plurality of orthogonal waveformshaving the same power spectral density profile, but their phase profilesacross a frequency span cause the plurality of orthogonal waveforms tobe orthogonal. For example, the phase of a first orthogonal waveform cancorrespond to the phase of a second orthogonal waveform rotated an evenmultiple of 2π radians across its bandwidth. Alternatively, theplurality of orthogonal waveforms can have phase shifts in accordancewith a plurality of Walsh functions. The, plurality of orthogonalwaveforms can also comprise n orthogonal waveforms phase shifted by 0 orπ radians in accordance with a plurality of n-bit Walsh functions.Additionally, a first orthogonal waveform of the plurality of orthogonalwaveforms can be the Hilbert transform of a second orthogonal waveformof the plurality of orthogonal waveforms. Each orthogonal waveform ofthe plurality of orthogonal waveforms can also be an n^(th) orderderivative of a first orthogonal waveform of the plurality of orthogonalwaveforms.

In another exemplary embodiment, the desired waveform can be modulatedin accordance with at least one of an information signal and a code.Thus, the time profile of the desired waveform can be modulated inaccordance with at least one of an information signal and a code. Thetime profile can be time limited and/or frequency limited.

Multi-band Signals

The waveform generator of the present invention may produce aggregate RFenergy confined to a one or more frequency bands within a largerfrequency band of interest. In one exemplary embodiment, the largerfrequency band of interest may be subdivided into a plurality of bandseach having the same bandwidth, e.g., 500 MHz, which corresponds to thebandwidth of aggregate RF energy that may be present within each band.As such, the larger frequency band of interest encompasses multiplebands.

In one embodiment of the invention, signals corresponding to each bandare individually defined by a different plurality of sample values. Forexample, a larger frequency band of interest may include four bands eachhaving a 500 MHz bandwidth at −10 dB that have center frequencies at 3.5GHz, 4 GHz, 4.5 GHz, and 5 GHz. In accordance with the invention, aprototype signal could be defined for each band. The prototype signalcorresponding to the first band could have a 3.5 GHz carrier frequencyand could be sampled at 7.0 GHz. The prototype signal corresponding tothe second band could have a 4.0 GHz carrier frequency and could besampled at 8.0 GHz. The prototype signal corresponding to the third bandcould have a 4.5 GHz carrier frequency and could be sampled at 9.0 GHzand the prototype signal corresponding to the fourth band could have a5.0 GHz carrier frequency and could be sample at 10.0 GHz. Under thisarrangement, a bandpass filter could optionally be used to limit energyof the transmitted signal to frequencies in a frequency band of interestbetween 3 GHz and 5.5 GHz. Because of the sampling rates used, harmonicswould fall outside the frequency band of interest and fold images wouldnot be produced. Thus, sample values corresponding to the four frequencybands could be used selectively by the multi-band system to switch fromband to band.

In another embodiment of the invention, fundamental spectra, harmonicsof the fundamental spectra, and fold images of the fundamental spectraand of the harmonics are purposely produced to occur in the variousbands used by a multi-band system and filters are used to limittransmitted energy to selected bands. For example, in FIG. 54, theprototype signal 410 of FIG. 41 is shown sampled at a 2 GHz samplingrate. Impulses generated in accordance with the samples 540 of FIG. 54have the frequency profile depicted in FIG. 55. In FIG. 55, fundamentalspectra 550 of the generated impulses is substantially the same as thefrequency profile 420 of the prototype signal 410. Fundamental spectra550 as well as harmonics 551, 552, and 553 of the fundamental spectraand fold images 554, 555, and 556 are within an exemplary frequency bandof interest 557 from 3 GHz to 10 GHz. Harmonics of the fundamentalspectra and fold images that are outside of the frequency band ofinterest 557 are ignored since they are to be removed by filtering. Thefundamental spectra 550, harmonics 551, 552, and 553, and fold images554, 555, and 556 can correspond to seven multi-band signals each havinga 500 MHz bandwidth at −10 dB. One skilled in the art will recognizethat one or more of the seven multi-band signals can be selected fortransmission by using filters to eliminate those signals not selectedfor transmission. The filtering can be varied over time to switch fromband to band. In one embodiment, filters are employed in accordance witha frequency band hopping code that defines a communications channel.

Communication Systems

Transmitters, Receivers, and Transceivers

The present invention can be used in systems comprising a transmitterand a direct conversion receiver. FIG. 56 depicts a transmitter 5600 anda direct conversion receiver 5602 each including the waveform generator390 previously described in relation, to FIG. 39. It should be notedthat the optional bandpass filter 398 of FIG. 39 has been replaced withoptional high-pass filter 5604 and low-pass filter 5606. The transmitter5600 of FIG. 56 produces a plurality of RF waveforms scaled inaccordance with an envelope and modulated by a data signal. Theplurality of RF waveforms is filtered to remove frequencies below andabove a desired frequency band, the filtered waveform is amplified byoperational amplifier 5608, and it is then transmitted using transmitantenna 5610. The transmitted signal is received at receive antenna5612, amplified with operational amplifier 5614 and the received signalis correlated with a template signal in mixer 5616. The template signalcan be the substantially similar to the filtered waveform produced bythe transmitter or may be somewhat different to account for expectedchanges between the transmitted signal and the received signal resultingfrom the transmit antenna 5610, receive antenna 5612, the multipathenvironment, etc. Integrator 5618 then integrates the output of mixer5616 and its output is demodulated to produce a baseband outputcorresponding to the data signal. The correlation of the received signalwith the template signal can be described as a direct conversion processsince the received signal is converted directly from a received signalto a baseband signal. One skilled in the art will understand that thetiming of RF waveforms generated in the receiver 5602 must be adjustedso that the template signal and received signal substantially coincidein mixer 5616. In other words, the programmable timer of waveformgenerator 390 of receiver 5602 would be affected as to acquire and trackthe received signal.

FIG. 57 shows a transceiver 5700 including a transmitter 5702 and areceiver 5704 that use the waveform generation method describedpreviously in relation to FIG. 50. The transmitter 5702 transmits afiltered waveform produced by combining and filtering two pluralities ofRF waveforms where the a first waveform generator 5002 generates a firstplurality of RF waveforms and the second waveform generator 5004generates a second plurality of RF waveforms offset in time from thefirst plurality of RF waveforms by a defined delay. A first memory 5016and a second memory 5018 store the first sample and second sample,respectively, of sample pairs determined in accordance with oneembodiment of the invention. DACs 5012 and 5014 produce analog signalsscaled in accordance with the stored sample values and thereby determinethe amplitude of impulses generated by the waveform generators. Acombiner 5008 combines the two pluralities or RF waveforms into a singleplurality of RF waveforms that is optionally filtered by bandpass filter5010. The filtered waveform (or optionally, the unfiltered plurality ofRF waveforms) is directed by transmit/receive switch 5706 to the eitheroperational amplifier 5608 and transmit antenna 5610 of transmitter 5702for transmission or to mixer 5616 of receiver 5704 for use as a templatesignal to correlate with the received signal. The direct conversionoperation of the receiver 5704 is the same as previously described forthe receiver 5602 of FIG. 56.

FIG. 58 presents an alternative waveform generator 5800 that can be usedin place of the waveform generators 5002 and 5004 of FIG. 57, wheredelay 5006 will continue to determine a time offset between the firstplurality of RF waveforms generated by a first waveform generator 5800and the second plurality of RF waveforms generated by a second waveformgenerator 5800. Each waveform generator 5800 uses a summer 5802 tocombine the output of three current sources 5806 that, when driven bypositive bits from 8×4 bit memory 5808, output 1×i, 2×i, and 4×icurrents, where i is some current amount. Thus, depending on the bitsoutput by memory 5808, the output of summer 5802 can be 0×i, 1×i, 2×i,3×i, 4×i, 5×i, 6×i, or 7×i. The output of summer 5802 is mixed by mixer5804 with either a positive or negative ½ cycle pulse depending on thepolarity determined by the polarity select bit output by memory 5808 andthe BPSK input. Thus, mixer 5804 outputs the first plurality (or second)plurality of RF waveforms scaled in accordance with the invention. Oneskilled in the art will recognize that memory 5808 is sized to defineeight different impulses and that the memory can be sized differentlydepending on the number of RF waveforms to be generated.

FIGS. 59 through 62 present four alternative direct conversion receivershaving alternative circuits for generating scaled RF waveforms based onstored data bits D0, D1, D2, and D4, which define sample values inaccordance with the invention. In FIG. 59, a received signal 5900 and animpulse produced by impulse generator 5901 is mixed in mixer 5902. Afteramplification by operational amplifier 5904, the output of mixer 5902may be attenuated by resistance ladder 5906 depending on data bits D0,D1, D2, and D4 before being integrated by integrator 5908.

The receiver of FIG. 60 is similar to the receiver of FIG. 59 exceptthat it uses a network 6000 of three current sources that are or are notshorted depending on data bits D1, D2, and D4 in order to attenuate theoutput of the operational amplifier 5904. When D0 is low, the currentsources are shorted out to produce a zero output voltage. Thisarrangement could alternatively be implemented by selectively enablingeach current source.

The receiver of FIG. 61 operates in a manner similar to the receivers ofFIGS. 59 and 60, but has a single current source 6100 that is attenuatedusing shunts 6102 based on data bits D0, D1, D2, and D4.

The receiver of FIG. 62 separately mixes received signal 5900 with up tothree impulses having the same voltage that are enabled based on bitsD1, D2, and D4. Impulse generators 5901 a, 5901 b, and 5901 c areindividually enabled by bits D1, D2, and D4, respectively, and theiroutput is mixed with received signal 5900 in mixers 5902 a, 5902 b, and5902 c. The outputs of mixers 5902 a, 5902 b, and 5902 c are separatelyintegrated in integrators 5908 a, 5908 b, and 5908 c. The outputs ofintegrators 5908 a, 5908 b are then weighted by weighting elements 6200a and 6200 b and then weighted outputs are summed by summer 6202. Thereceiver of FIG. 62 has the advantage of analog processing at themaximum level.

FIG. 63 depicts a circuit implementing a weighted summer with anembedded 3-bit DAC, while FIG. 64 shows a circuit implementing adifferentially weighted summer with a 4-bit DAC.

Multi-band Communication Systems

FIG. 65 presents a multi-band transmitter embodiment of the inventionemploying a memory sized to define signals for four bands. Thetransmitter uses the sample pair approach as described in relation toFIG. 50 and weighted DAC summer approach. FIG. 66 presents amulti-receiver embodiment intended to complement the 4 band transmitterof FIG. 65. The receiver of FIG. 65 has four separate integrators havingoutputs that are weighted and then summed.

FIG. 67 presents an alternative waveform generator that can be used in amulti-band transmitter or receiver. It involves a phase lock loop-basedwaveform generator used to produce a train of impulses that areamplitude modulated by mixing them with the output of a DAC. Theresultant weighted train is filtered to produce a waveform resembling anenveloped carrier having a center frequency within the appropriate band.

FIG. 68 presents another waveform generator approach that can be used ina multi-band transmitter or receiver. It involves separately clockedimpulse generators that are weighted in accordance with DACs and thesummed impulses are then summed.

Waveform Synthesis Analyzer Software

The primary display of the Waveform Synthesis Analyzer software isdepicted in FIG. 69. It includes a waveform plot, a spectra plot, andsoftware controls. The waveform plot is used to depict the prototypesignal (or desired waveform), samples of the prototype signal, and theplurality of RF waveforms to be generated to synthesize the prototypesignal. The spectra plot is used to depict the energy spectra of theprototype signal and of the plurality of RF waveforms. The softwarecontrols are primarily used to define characteristics of the prototypesignal such as its bandwidth and center frequency, envelope shape, etc.,to define sampling characteristics, and to define the characteristics ofthe RF waveforms that would be generated to synthesize the prototypesignal.

FIG. 70 depicts an output window of the Waveform Synthesis Analyzersoftware that is used to compare the time profile of the prototypesignal to the time profile of the plurality of RF waveforms if they arefiltered, which is an optional feature of the invention. FIG. 71 depictsthe values of the samples used to scale the plurality or RF waveforms asdefined by the software controls.

It will be apparent to one skilled in the art that the detaileddescription of the invention disclosed herein comprises exemplaryembodiments of the invention and that modifications may be made withoutdeparting from the teachings of the invention. Accordingly, theembodiments disclosed herein should be understood to only berepresentative and that the scope of the present invention should onlybe limited by the claims included herein and their equivalents.

1. A method of emulating a desired waveform, comprising: producing atime profile of said desired waveform characterized by a plurality ofsample values; generating a plurality of RF waveforms, each RF waveformsare generated in accordance with a timing of a plurality of samplescorresponding to said plurality of sample values, wherein the pluralityof RF waveforms are generated in one or more groups, each group of theone or more groups comprising two or more RF waveforms having apredefined time spacing, wherein at least one RF waveform of each groupis inverted, wherein the predefined time spacing corresponds to onefourth of the period of a frequency of an eliminated fold image.
 2. Amethod of emulating a desired waveform, comprising: producing a timeprofile of said desired waveform characterized by a plurality of samplevalues; generating a plurality of RF waveforms, each RF waveforms aregenerated in accordance with a timing of a plurality of samplescorresponding to said plurality of sample values, wherein said pluralityof RF waveforms are generated in accordance with a timing of a pluralityof samples corresponding to said plurality of sample values, wherein thetime spacing between the plurality of RF waveforms corresponds to thetime spacing between the plurality of samples.
 3. A method of emulatinga desired waveform, comprising: producing a time profile of said desiredwaveform characterized by a plurality of sample values; generating aplurality of RF waveforms, each RF waveforms are generated in accordancewith a timing of a plurality of samples corresponding to said pluralityof sample values, wherein said plurality of RF waveforms are generatedin accordance with a timing of a plurality of samples corresponding tosaid plurality of sample values, wherein the time spacing of theplurality of samples is substantially equal corresponding to ageneration rate of the plurality of RF waveforms.
 4. The method of claim3, wherein the generation rate corresponds to a desired center frequencywithin a frequency band of interest.
 5. The method of claim 3, whereinthe generation rate is programmable.
 6. A method of emulating a desiredwaveform, comprising: producing a time profile of said desired waveformcharacterized by a plurality of sample values; generating a plurality ofRF waveforms, each RF waveforms are generated in accordance with atiming of a plurality of samples corresponding to said plurality ofsample values, wherein the time profile is in accordance with a shiftedaverage DC level of the desired waveform.
 7. The method of claim 6,wherein the shifted average DC level is shifted such that each of theplurality of samples has the same polarity.
 8. The method of claim 6,further comprising removing a DC component from an aggregate RF energyspectra.
 9. A method of emulating a desired waveform, comprising:producing a time profile of said desired waveform characterized by aplurality of sample values; generating a plurality of RF waveforms, eachRF waveforms are generated in accordance with a timing of a plurality ofsamples corresponding to said plurality of sample values, wherein thetime profile of the desired waveform corresponds to a composite profileof a plurality of orthogonal waveforms, wherein the plurality oforthogonal waveforms have phase shifts in accordance with a plurality ofWalsh functions.
 10. The method of claim 9, wherein the plurality oforthogonal waveforms comprises n orthogonal waveforms phase shifted by 0or π radians in accordance with a plurality of n-bit Walsh functions.11. A method of emulating a desired waveform, comprising: producing atime profile of said desired waveform characterized by a plurality ofsample values; generating a plurality of RF waveforms, each RF waveformsare generated in accordance with a timing of a plurality of samplescorresponding to said plurality of sample values, wherein the timeprofile of the desired waveform corresponds to a composite profile of aplurality of orthogonal waveforms, wherein a first orthogonal waveformof the plurality of orthogonal waveforms is the Hilbert transform of asecond orthogonal waveform of the plurality of orthogonal waveforms. 12.A method of emulating a desired waveform, comprising: producing a timeprofile of said desired waveform characterized by a plurality of samplevalues; generating a plurality of RF waveforms, each RF waveforms aregenerated in accordance with a timing of a plurality of samplescorresponding to said plurality of sample values, wherein the timeprofile of the desired waveform corresponds to a composite profile of aplurality of orthogonal waveforms, wherein each orthogonal waveform ofthe plurality of orthogonal waveforms is an n^(th) order derivative of afirst orthogonal waveform of the plurality of orthogonal waveforms. 13.A method of emulating a desired waveform, comprising: producing a timeprofile of said desired waveform characterized by a plurality of samplevalues; generating a plurality of RF waveforms, each RF waveforms aregenerated in accordance with a timing of a plurality of samplescorresponding to said plurality of sample values, wherein the timeprofile is produced by an inverse Fourier transformation of a freQuencyprofile of the desired waveform, wherein the frequency profile isproduced by a Fourier transformation of a vector amplitude profile ofthe desired waveform, wherein the vector amplitude profile comprises x,y, z, t, amplitude, and vector polarization angle parameters, wherein x,y, and z correspond to location coordinates, and wherein one or moreparameters of said x, y, z, t, amplitude, and vector polarization angleparameters is maintained constant to define at least one of signalamplitude and polarization atone of a point, line, plane, and surface inspace over time relative to a position.
 14. The method of claim 13,wherein the position is a transmit antenna position.
 15. A method forgenerating waveforms, comprising: generating a plurality of RF waveformsat a waveform generation rate; and modulating the plurality of RFwaveforms in accordance with samples of a time profile of a prototypesignal to produce an aggregate RF energy that approximates the RF energyof the prototype signal; generating a first plurality of RF waveforms inaccordance with corresponding samples of the time profile; andgenerating a second plurality of RF waveforms in accordance withcorresponding samples of the time profile, wherein there is a definedtime spacing between each of the second plurality of RF waveforms and acorresponding one of the first plurality of RF waveforms, wherein thedefined time spacing corresponds substantially to one fourth of a rateat which both the first plurality of RF waveforms and second pluralityof RF waveforms are generated.
 16. A waveform generator, comprising: asignal generator that generates a plurality of RF waveforms at awaveform generation rate, each of said plurality of RF waveforms havingan amplitude scaled in accordance with a desired envelope of a prototypesignal; and a filter that limits the aggregate RF energy of theplurality of RF waveforms to within a frequency band of interest,wherein the signal generator includes: a first signal generator thatgenerates a first plurality of RF waveforms having amplitudes modulatedin accordance with the desired envelope; a second signal generator thatgenerates a second plurality of RF waveforms having amplitudes modulatedin accordance with the desired envelope, wherein there is a defined timespacing between each of the second plurality of RF waveforms and acorresponding one of the first plurality of RF waveforms, wherein thedefined time spacing corresponds substantially to one fourth of a rateat which both the first plurality of RF waveforms and second pluralityof RF waveforms are generated.